Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901The extended irregular domination problem7177371487010.22049/cco.2024.30046.2289ENLorenzoMellaDip. di Scienze Fisiche, Informatiche, Matematiche,
Universitá degli Studi di Modena e Reggio Emilia,
Via Campi 213/A, I-41125 Modena, ItalyAnitaPasottiDICATAM - Sez. Matematica, Universitá degli Studi di Brescia,
Via Branze 43, I-25123 Brescia, ItalyJournal Article20241007In this paper we introduce a new domination problem strongly related to the following one recently proposed by Broe, Chartrand and Zhang. One says that a vertex $v$ of a graph $\Gamma$ labeled with an integer $\ell$ dominates the vertices of $\Gamma$ having distance $\ell$ from $v$. An irregular dominating set of a given graph $\Gamma$ is a set $S$ of vertices of $\Gamma$, having distinct positive labels, whose elements dominate every vertex of $\Gamma$. Since it has been proven that no connected vertex transitive graph admits an irregular dominating set, here we introduce the concept of an \emph{extended} irregular dominating set, where we admit that precisely one vertex, labeled with 0, dominates itself. Then we present existence or non existence results of an extended irregular dominating set $S$ for several classes of graphs, focusing in particular on the case in which $S$ is as small as possible. We also propose two conjectures. https://comb-opt.azaruniv.ac.ir/article_14870_c288dce3f5a09781bc4edd1e96a1ffce.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901Weak signed double Roman domination in graphs7397561487110.22049/cco.2024.30016.2268ENLutzVolkmannRWTH Aachen University, 52056 Aachen, GermanyJournal Article20240918A weak signed double Roman dominating function (WSDRDF) of a graph $G$ with vertex set $V(G)$ is defined as a function $f:V(G)\rightarrow\{-1,1,2,3\}$ having the property that $\sum_{x\in N[v]}f(x)\ge 1$ for each $v\in V(G)$, where $N[v]$ is the closed neighborhood of $v$. The weight of a WSDRDF is the sum of its function values over all vertices. The weak signed double Roman domination number of $G$, denoted by $\gamma_{wsdR}(G)$, is the minimum weight of a WSDRDF in $G$. We initiate the study of the weak signed double Roman domination number, and we present different sharp bounds on $\gamma_{wsdR}(G)$. In addition, we determine the weak signed double Roman domination number of some classes of graphs.https://comb-opt.azaruniv.ac.ir/article_14871_be0d2fde325e3b695f9f4ab3fec3dc9a.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901Seidel energy of a graph with self-loops7577661484210.22049/cco.2024.29576.2062ENHarshithaADepartment of Mathematics, Manipal Institute of Technology Bengaluru,
Manipal Academy of Higher Education, Manipal, India - 560064SabithaD'SouzaDepartment of Mathematics, Manipal Institute of Technology,
Manipal Academy of Higher Education, Manipal, India, 576104SwatiNayakDepartment of Mathematics, Manipal Institute of Technology,
Manipal Academy of Higher Education, Manipal, India, 576104IvanGutmanFaculty of Science, University of Kragujevac, 34000 Kragujevac, SerbiaJournal Article20240319Let $G_S$ be a graph obtained by attaching a self-loop to each vertex of $S\subseteq V$ of a graph $G(V,E)$. The Seidel matrix of $G_S$ is $S(G_S)=[s_{ij}]$, where $s_{ij}=-1$ if $v_i$ and $v_j$ are adjacent and $v_i\in S$, $s_{ij}=1$ if $v_i$ and $v_j$ are non-adjacent, and it is zero if $i=j$ and $v_i\not\in S$. If $\theta_i(G_S)\,,\,i=1,2,\ldots,n$, are the eigenvalues of the Seidel matrix, then the Seidel energy of the graph $G_S$, containing $n$ vertices and $\sigma$ self-loops, is defined as $\sum_{i=1}^n \left|\theta_i(G_S)+\frac{\sigma}{n}\right|$. In this paper, some basic properties of Seidel energy of graphs containing self-loops are established.https://comb-opt.azaruniv.ac.ir/article_14842_6d32946bbdfd56c445b722f2d612baa4.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901On Connected Graphs with Integer-Valued Q-Spectral Radius7677861484710.22049/cco.2024.29278.1922ENJesminaPervinDepartment of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi-221005, IndiaLavanyaSelvaganeshDepartment of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi-221005, IndiaSmratiPandeyDepartment of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi-221005, IndiaJournal Article20231217The $Q$-eigenvalues are the eigenvalues of the signless Laplacian matrix $Q(G)$ of a graph $G$, and the largest $Q$-eigenvalue is known as the $Q$-spectral radius $q(G)$ of $G$. The edge-degree of an edge is defined as the number of edges adjacent to it. In this article, we characterize the structure of simple connected graphs having integral $Q$-spectral radius. We show that the necessary and sufficient condition for such graphs to contain either a double star $\mathcal{S}_{r}^{2}$ or its variation $\mathcal{S}_{r}^{2,1}$ (having exactly one common neighbor between the central vertices) as a subgraph is that the maximum edge-degree is $2r$, where $r= q(G) -3$. In particular, we characterize all graphs that contain only double star as a subgraph when $q(G)$ equals $8$ and $9$. Further, we characterize all the connected edge-non-regular graphs with a maximum edge-degree equal to $4$ whose minimum $Q$-eigenvalue does not belong to the open interval $(0,1)$ and has an integral $Q$-spectral radius.https://comb-opt.azaruniv.ac.ir/article_14847_92c0c4c101eb3908bc4f77ca725a7225.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901The Sombor index and multiplicative Sombor index of some products of graphs7878261487810.22049/cco.2024.30123.2321ENDilbak HajiMohammadDepartment of Mathematics, College of Science, University of Duhok,
Duhok, Kurdistan Region, IraqJournal Article20241103The Sombor index is a vertex degree-based topological index which it was de ned by Ivan Gutman in 2021. We study the Sombor index and the multiplicative Sombor index on some products of graphs, crown graphs, shelf graphs, Ice-cream graphs, helm graphs, ower graphs, generalized Sierpi<span class="title-text">ń</span>ski graphs, $t$-Mycielskian graphs, $t$-ciclo graphs, and $t$-estella graphs. Then we provide some upper and lower bounds for them.https://comb-opt.azaruniv.ac.ir/article_14878_601c007a4ff3cc209e1dcf3099dde52b.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901The monophonic pebbling number of neural networks with generalized algorithm and their applications8278421484810.22049/cco.2024.29481.2017ENK.C.KavithaDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of Technology
Vellore - 632014, Tamil Nadu, IndiaS.JagatheswariDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of Technology Vellore - 632014, Tamil Nadu, IndiaJournal Article20240224Consider a graph $\sigma$(V, E) with nodes V and edges E is a connected graph with some pebbles scattered over its nodes V. By removal of two pebbles from one node and placing one pebble to an adjacent node is a pebbling move. A monophonic pebbling number, $\lambda_{M}(\sigma, v)$, of a node v of a graph $\sigma$ is the least number $m$ such that minimum of one pebble could be shifted to v by a sequence of pebbling shifts for any distribution of $\lambda_{M}(\sigma, v)$ pebbles on the nodes of $\sigma$ using monophonic path. A link between the nodes x and y is an x-y path which consists of no chords and is monophonic. The monophonic pebbling number of a graph $\sigma$ is the highest $\lambda_{M}(\sigma, v)$ among all the nodes notated as $\lambda_{M}(\sigma)$. For the first time, we calculate the monophonic pebbling number on families of neural networks such as probabilistic neural networks(PNNs), convolutional neural networks(CVNNs), modular neural networks(MNNs), generalized regression neural networks(GRNNs) and Hopfield neural networks(HNNs) and discuss their applications. We give the generalized algorithm to find the monophonic pebbling number of any graph $\sigma$.https://comb-opt.azaruniv.ac.ir/article_14848_4121efbad41dff3eae036d4be2811bc4.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901Dominated chromatic number of some kinds of the generalized Helm graphs8438561487210.22049/cco.2024.29283.1924ENF.PoryousefiDepartment of Pure Mathematics and Center of Excellence in Analysis on Algebraic Structures,
Ferdowsi University of Mashhad,
P. O. Box 1159-91775, Mashhad, IranA.ErfanianDepartment of Pure Mathematics and Center of Excellence in Analysis on Algebraic Structures,
Ferdowsi University of Mashhad,
P. O. Box 1159-91775, Mashhad, IranM.NasiriDepartment of Pure Mathematics and Center of Excellence in Analysis on Algebraic Structures,
Ferdowsi University of Mashhad,
P. O. Box 1159-91775, Mashhad, IranJournal Article20231220Let $G$ be a simple graph. The dominated coloring of a graph $G$ is a proper coloring of $G$ such that each color class is dominated by at least one vertex. The minimum number of colors needed for a dominated coloring of $G$ is called the dominated chromatic number of $G$, denoted by $\chi_{dom}(G)$. The current study is devoted to investigate the dominated chromatic number of Helm graphs and some kinds of its the generalizations.https://comb-opt.azaruniv.ac.ir/article_14872_97756ae6a244eafa01c2007870935e69.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901On the rainbow connection number of the connected inverse graph of a finite group8578701485010.22049/cco.2024.29123.1848ENRian FebrianUmbaraDoctoral Program in Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, IndonesiaSchool of Computing, Telkom University, Bandung, Indonesia0000-0001-5950-5300A.N.M.SalmanCombinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, IndonesiaPritta EtrianaPutriCombinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, IndonesiaJournal Article20231031Let $\Gamma$ be a finite group with $T_\Gamma=\{t\in \Gamma \mid t\ne t^{-1} \}$. The inverse graph of $\Gamma$, denoted by $IG(\Gamma)$, is a graph whose vertex set is $\Gamma$ and two distinct vertices, $u$ and $v$, are adjacent if $u*v\in T_\Gamma$ or $v*u\in T_\Gamma$. In this paper, we study the rainbow connection number of the connected inverse graph of a finite group $\Gamma$, denoted by $rc(IG(\Gamma))$, and its relationship to the structure of $\Gamma$. We improve the upper bound for $rc(IG(\Gamma))$, where $\Gamma$ is a group of even order. We also show that for a finite group $\Gamma$ with a connected $IG(\Gamma)$, all self-invertible elements of $\Gamma$ is a product of $r$ non-self-invertible elements of $\Gamma$ for some $r\leq rc(IG(\Gamma))$. In particular, for a finite group $\Gamma$, if $rc(IG(\Gamma))=2$, then all self-invertible elements of $\Gamma$ is a product of two non-self-invertible elements of $\Gamma$. The rainbow connection numbers of some inverse graphs of direct products of finite groups are also observed.https://comb-opt.azaruniv.ac.ir/article_14850_c728ded1d0f0f7ee5ac55156c06605e5.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901Edge graceful labeling on neutrosophic graphs8718951486310.22049/cco.2024.28826.1740ENG.VetrivelDepartment of Mathematics, Alagappa University, Karaikudi, Tamilnadu, IndiaM.MullaiDepartment of Mathematics, Alagappa University, Karaikudi, Tamilnadu, IndiaJournal Article20230713In this article, the edge graceful labeling concept has been expanded from conventional fuzzy graphs to intuitionistic and neutrosophic graphs. There has been much discussion of the edge graceful labeling in intuitionistic and neutrosophic graphs with certain sequence of edge labels(for each membership) in clockwise or anticlockwise direction and the resultant vertices. Also, various irregular properties and application of neutrosophic edge graceful labeling graphs have been discussed in detail.https://comb-opt.azaruniv.ac.ir/article_14863_e4681c59b522841c30c8cdbabe3f7493.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901Degree–based topological indices of a general random chain8979091487310.22049/cco.2024.30080.2301ENSayléSigarretaFacultad de Ciencias F´ısico Matemáticas, Benemérita Universidad Autónoma de Puebla,
Puebla, MéxicoHugoCruz SuárezFacultad de Ciencias F´ısico Matemáticas, Benemérita Universidad Autónoma de Puebla,
Puebla, MéxicoSergioTorralbas FitzDepartment of Orthopedic Oncology, University of Miami - Miller School of Medicine, Miami, Florida, United StatesJournal Article20241020In this paper, we examine a specific type of random chains and propose a unified approach to studying the degree-based topological indices, including their extreme values. We derive explicit analytical expressions for the expected values and variances of these indices and we establish the asymptotic behavior of the indices. Specifically, we analyze the first Zagreb index, Sombor index, harmonic index, Geometric-Arithmetic index, Inverse Sum Index, and the second Zagreb index for various general random chains, including random phenylene, random polyphenyl, random hexagonal, and linear chains. https://comb-opt.azaruniv.ac.ir/article_14873_f023138f1d463d6aa1bc82f49dbe4979.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901Extremal trees for the general Sombor index9119221486610.22049/cco.2024.29444.1996ENChinglensanaPhanjoubamDepartment of Mathematics, North-Eastern Hill University, Shillong, IndiaSainkupar MnMawiongDepartment of Basic Sciences and Social Sciences, North-Eastern Hill University, Shillong, IndiaArdeline M.BuhphangDepartment of Mathematics, North-Eastern Hill University, Shillong, IndiaJournal Article20240211Recently, the Sombor index of a graph has been extended to general Sombor index. The general Sombor index of a simple graph $G$ is defined as $SO_\alpha(G)=\displaystyle\sum_{uv\in E(G)}[d_G(u)^2+d_G(v)^2]^{{\alpha}/2}$, where $d_G(u)$ denotes the degree of a vertex $u$ in $G$ and $\alpha$ is a real number. In this paper, we obtain bounds for the general Sombor index of trees. We further determine the trees with the extremal general Sombor indices.https://comb-opt.azaruniv.ac.ir/article_14866_a0357e603986d2b1c3924744c5da59fd.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901A new approach for solving multi-objective interval-valued variational problems and its applications9239391486410.22049/cco.2024.29824.2173ENShubhamSinghSchool of Advanced Sciences, VIT-AP University, Amaravati, Vijaywada, 522237, Andhra Pradesh, IndiaShaliniJhaSchool of Advanced Sciences, VIT-AP University, Amaravati, Vijaywada, 522237, Andhra Pradesh, IndiaJournal Article20240611This study focuses on one of the methods for solving a nonlinear multiobjective convex interval-valued variational problem. Namely, the weighting method is used to find its weakly $LU$-efficient solution and $LU$-efficient solution. Therefore, the weighted variational problem is introduced for the given nonlinear multiobjective interval-valued variational problem. Then, under appropriate convexity assumptions, the equivalance between a (weakly) $LU$-efficient solution of the original nonlinear multiobjective interval-valued variational problem and an optimal solution of its associated weighting variational problem is established.https://comb-opt.azaruniv.ac.ir/article_14864_70d9205d8ee96caaa372240cfa35c028.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901On norms, spread, characteristic polynomial and determinant of Hankel and Toeplitz matrices with Mersenne sequence9419581487610.22049/cco.2024.30037.2287ENKalikaPrasadDepartment of Applied Science and Humanities (Mathematics),
Government Engineering College Bhojpur, Bihar, India, 8023010000-0002-3653-5854MuneshKumariDepartment of Applied Science and Humanities (Mathematics),
Government Engineering College Bhojpur, Bihar, India, 802301JagmohanTantiDepartment of Mathematics, Babasaheb Bhimrao Ambedkar University, Lucknow, India, 2260250000-0002-0078-7494Journal Article20241002In this work, some new properties of the Hankel and Toeplitz matrices are obtained by considering the Mersenne numbers as entries. We developed efficient formulas to compute matrix norms like $\|.\|_1$, $\|.\|_\infty$, Euclidean norm, spread, and the lower and upper bound for the spectral norm of these matrices. Also, the study shows that these matrices are non-singular for $n=2$ and singular for $n\geq 3$. Furthermore, we presented rank, eigenvalues, principal minors, and the characteristic polynomial of them explicitly.https://comb-opt.azaruniv.ac.ir/article_14876_e301d3063751d0a3d95c7843c5d4640b.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901The minimum Zagreb indices for unicyclic graphs with fixed Roman domination number9599731486710.22049/cco.2024.29846.2188ENFatemeMovahediDepartment of Mathematics, Faculty of Sciences, Golestan University, Gorgan, IranAyu Ameliatul ShahilahAhmad JamriSpecial Interest Group on Modelling and Data Analytics (SIGMDA),
Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu,
21030 Kuala Nerus, Terengganu, MalaysiaRoslanHasniSpecial Interest Group on Modelling and Data Analytics (SIGMDA),
Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu,
21030 Kuala Nerus, Terengganu, MalaysiaMohammadhadiAkhbariDepartment of Mathematics, Estahban Branch, Islamic Azad University, Estahban, IranHailizaKamarulhailiSchool of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Penang, MalaysiaJournal Article20240624Let $G=(V, E)$ be a graph with the vertex set $V$ and the edge set $E$. The first Zagreb index of a graph $G$ is defined to be the sum of squares of degrees of all the vertices of the graph. The second Zagreb index of the graph $G$ is the sum of the $d(u)d(v)$ for every edge $uv \in E$, where $d(u)$ and $d(v)$ denote the degree of the vertices $u, v \in V$. In this paper, we propose new lower bounds of the Zagreb indices of unicyclic graphs in terms of the order and the Roman domination number. We prove that $4n-2\left(\gamma_{R}-\left\lceil\dfrac{2n}{3}\right\rceil\right)$ and $4n-3\left(\gamma_{R}-\left\lceil\dfrac{2n}{3}\right\rceil\right)$ are the sharp lower bounds for the first Zagreb index and the second Zagreb index, respectively. Also, we characterize the extremal trees for these lower bounds.https://comb-opt.azaruniv.ac.ir/article_14867_02da586fd53300ff836f994ef621d9f7.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901Algorithm for describing the Terwilliger and quantum adjacency algebras of a distance-regular graph9759841487410.22049/cco.2024.29114.1874ENAbdillahAhmadMaster Program in Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, IndonesiaJohn VincentMoralesDepartment of Mathematics and Statistics, De La Salle University, Manila, PhilippinesPritta EtrianaPutriCombinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, IndonesiaJournal Article20231110In this paper we consider an algorithm for determining a basis for the Terwilliger and quantum adjacency algebras of a distance-regular graph. For the Terwilliger algebra, we consider the generating set. For the quantum adjacency algebra, we consider the generating set consisting of the raising, flat, and lowering matrices. We give optimization method by using generating matrices with a block-matrix structure so that the number of matrix multiplications required is reduced.https://comb-opt.azaruniv.ac.ir/article_14874_806405ed152175692394b8ae0ff3594e.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901A construction of cospectral signed line graphs9859931487710.22049/cco.2024.30034.2284ENZoranStanićFaculty of Mathematics, University of Belgrade, Studentski trg 16, 11 000 Belgrade, SerbiaJournal Article20240930For an ordinary graph $G$, we compute the eigenvalues and the eigenspaces of the signed line graph $\mathcal{L}(\ddot{G})$, where $\ddot{G}$ is obtained from $G$ by inserting a negative parallel edge between every pair of adjacent vertices. As an application, we prove that if $G$ and $H$ share the same vertex degrees, then $\mathcal{L}(\ddot{G})$ and $\mathcal{L}(\ddot{H})$ share the same spectrum. To the best of our knowledge, this construction does not follow the line of any known construction developed for either graphs or signed graphs. Among the other consequences, we emphasize that $\mathcal{L}(\ddot{G})$ is integral (i.e., its spectrum consists entirely of integers), which means that a construction of integral signed graphs has been established simultaneously.https://comb-opt.azaruniv.ac.ir/article_14877_f7086ec79f356f1b2522fdc3733cdc57.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901On $k$-(total) limited packing in graphs99510111488810.22049/cco.2025.29709.2125ENAzam SadatAhmadiDepartment of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, IranNasrinSoltankhahDepartment of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, IranJournal Article20240506A set $B\subseteq V(G)$ is called a $k$-total limited packing set in a graph $G$ if $|B\cap N(v)|\leq k$ for any vertex $v\in V(G)$. The $k$-total limited packing number $L_{k,t}(G)$ is the maximum cardinality of a $k$-total limited packing set in $G$. Here, we give some results on the $k$-total limited packing number of graphs emphasizing trees, especially when $k=2$. We also study the $2$-(total) limited packing number of some product graphs. <br /><br /><br /><br />A $k$-limited packing partition ($k$LPP) of graph $G$ is a partition of $V(G)$ into $k$-limited packing sets. The minimum cardinality of a $k$LPP is called the $k$LPP number of $G$ and is denoted by $\chi_{\times k}(G)$, and we obtain some results for this parameter.https://comb-opt.azaruniv.ac.ir/article_14888_0aa580287ee727be161ab97a0477d721.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901Geometric-arithmetic index-energy predicting the physical properties of alkanes101310321487910.22049/cco.2024.28999.1807ENBilal AhmadRatherDepartment of Mathematics, Samarkand International University of Technology, Samarkand 140100, UzbekistanM.AouchichePolytechnique Montreal, Montreal, QC, CanadaM.ImranDepartment of Mathematical and Natural Sciences, Prince Mohammad Bin Fahd University,
P.O. Box 1664, Al Khobar 31952, Saudi ArabiaS.MondalRISE, MASEP Group, University of Sharjah, Sharjah 27272, UAEJournal Article20230918The topological indices play a crucial role in generating the weighted adjacency matrix, which exhibits significant diversity from both theoretical and application perspectives compared to the ordinary adjacency matrix. One such notable weighted matrix is the geometric-arithmetic matrix, generated from the well-known $GA$ (geometric-arithmetic) index. Here, we focus on a comparative study of the $GA$ index and the geometric-arithmetic energy $\mathcal{GAE}$. We establish several tight bounds on $\mathcal{GAE}$ involving various graph invariants and identify the corresponding extremal graphs. Additionally, we compare the correlation of the molecular property Bp (boiling point) with $GA$ and $\mathcal{GAE}$. Our findings reveal that the Bp shows good correlation with $\mathcal{GAE}$ than with $GA$ index. Furthermore, we examine the role of $\mathcal{GAE}$ in explaining different properties of drugs associated with kidney disease.https://comb-opt.azaruniv.ac.ir/article_14879_5d98d961611894f82bff67df74dc99ac.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901Roman domination value in graphs103310461488010.22049/cco.2024.28899.1769ENP. Roushini LeelyPushpamDepartment of Mathematics, D.B. Jain College, Chennai 600 097, Tamil Nadu, IndiaPadmaprieaSampathDepartment of Mathematics, Sri Sairam Engineering College, Chennai 600 044, Tamil Nadu, IndiaJournal Article20230803For a graph $G=(V,E)$, a set $S \subseteq V$ is a \textit{dominating set} if every vertex in $V\setminus S$ has a neighbour in $S$. The \textit{domination number}, denoted by $\gamma(G)$, is the minimum cardinality of a dominating set in $G$ and a dominating set of minimum cardinality is called a \textit{$\gamma(G)$-set}. Cockayne et al. defined a \textit{Roman dominating function} (RDF) on a graph $G = (V,E)$ to be a function $f:V\rightarrow \lbrace 0,1,2\rbrace$ satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v)=2$. The \textit{Roman domination number}, denoted by $\gamma_R(G)$, is the minimum weight of an RDF in $G$. An RDF of weight $\gamma_R(G)$ is called a \textit{$\gamma_R(G)$-function}. Eunjeong Yi introduced the \textit{domination value of $v$}, denoted by $DV_G(v)$, to be the number of $\gamma(G)$-sets to which $v$ belongs. In this paper, we extend the idea of domination value to Roman domination. For a vertex $v \in V$, we define the \textit{Roman domination value}, denoted by $R_G(v)$, as $ R_G(v) = \sum_{f \in \mathcal{F}} f(v)$, where $\mathcal{F}$ denote the set of all $\gamma_R(G)$-functions. We also study some basic properties of Roman domination value of vertices for a given graph and determine the Roman domination value for the vertices of a complete $k$-partite graph.https://comb-opt.azaruniv.ac.ir/article_14880_bbe95ffa92249d4b7a71766b84723aa1.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901Strong global distribution center of graphs104710571488110.22049/cco.2025.29903.2217ENMostafaEdalatDepartment of Basic Sciences, Shahid Rajaee Teacher Training University,
P.O. Box 16785-163, Tehran, IranHamidrezaMaimaniDepartment of Basic Sciences, Shahid Rajaee Teacher Training University,
P.O. Box 16785-163, Tehran, IranJournal Article20240720Let $G=(V,E)$ be a graph. A strong global distribution center of $G$ is a dominating set $S\subseteq V$ such that for any $v\in V\setminus S$, there exists a vertex $u\in N[v]\cap S$ with the property $|N[u]\cap S|> |N[v]\cap (V\setminus S)|$. The strong global distribution center number, gdc$^s(G)$, of a graph $G$ is the minimum cardinality of a strong global distribution center of $G$. In this paper, we introduce the concept of strong global distribution center. We give some bounds on the gdc$^s(G)$ for general graphs and classify graphs with extremal values of gdc$^s(G)$. Also, we compute the strong global distribution center number for some families of graphs and study this parameter for some families of graph products.https://comb-opt.azaruniv.ac.ir/article_14881_2f3c20535e87868ce1f5c1a0cef23d51.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-212811320260901On Hermite-Hadamard Type Inequalities in Stochastic Fractional Calculus105910711507610.22049/cco.2025.30980.2689ENAsraaNajm AboodDepartment of Mathematics, College of Dentistry, Diyala University, Diyala, IraqRawaa KhalilIbrahimDepartment of Mathematics, College of Dentistry, University of Diyala, Diyala, IraqJournal Article20250908This paper extends Hermite-Hadamard type inequalities within the framework of stochastic fractional calculus. We investigate how fractional integrals, which account for memory effects, interact with random processes. Our work presents three main contributions. First, we provide an error bound for approximating a standard integral of a smooth, deterministic function using stochastic fractional integrals. Second, we extend the well-known Hermite-Hadamard inequality, which applies to convex functions, to the setting of convex stochastic processes, showing how their expected values are bounded by these integrals. Finally, we derive specific mean-square error bounds when approximating a standard Brownian motion using its stochastic fractional integrals. These results enhance our understanding of stochastic fractional inequalities, offering new tools for analyzing complex systems influenced by both memory and randomness.https://comb-opt.azaruniv.ac.ir/article_15076_d59e0a6111c47b0ff2c87c9134bf06e0.pdf