Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288420231231Time-subinterval shifting in zero-sum games played in staircase-function finite and uncountably infinite spaces6036291451710.22049/cco.2023.27717.1326ENVadimRomanukeFaculty of Mechanical and Electrical Engineering, Polish Naval Academy, Gdynia, PolandJournal Article20220310A tractable and efficient method of solving zero-sum games played in staircase-function finite spaces is presented, where the possibility of varying the time interval on which the game is defined is considered. The time interval can be narrowed by an integer number of time subintervals and still the solution is obtained by stacking solutions of smaller-sized matrix games, each defined on a subinterval where the pure strategy value is constant. The stack is always possible, even when only time is discrete and the set of pure strategy possible values is uncountably infinite. So, the solution of the initial discrete-time staircase-function zero-sum game can be obtained by stacking the solutions of the ordinary zero-sum games defined on rectangle, whichever the time interval is. Any combination of the solutions of the subinterval games is a solution of the initial zero-sum game.http://comb-opt.azaruniv.ac.ir/article_14517_28c9b6bd8063b0d70892e4db7e9f4b22.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288420231231Domination parameters of the splitting graph of a graph6316371442010.22049/cco.2022.27871.1376ENDeepalakshmiJDepartment of Mathematics,
Madurai Kamaraj University,
Madurai,
Tamilnadu, IndiaMarimuthuGDepartment of Mathematics,
The Madura College,
Madurai,
Tamilnadu, IndiaSomasundaramArumugamBirla Institute of Technology and Sciences Pilani, Dubai CampusSubramanianArumugamDirector (n-CARDMATH)
Kalasalingam University
Anand Nagar, Krishnankoil-626 126
Tamil Nadu, India0000-0002-4477-9453Journal Article20220508Let $G=(V,E)$ be a graph of order $n$ and size $m.$ The graph $Sp(G)$ obtained from $G$ by adding a new vertex $v'$ for every vertex $v\in V$ and joining $v'$ to all neighbors of $v$ in $G$ is called the splitting graph of $G.$ In this paper, we determine the domination number, the total domination number, connected domination number, paired domination number and independent domination number for the splitting graph $Sp(G).$http://comb-opt.azaruniv.ac.ir/article_14420_4d6399393b193a1fc7c6aa59528b0b12.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288420231231The Cartesian product of wheel graph and path graph is antimagic6396471442410.22049/cco.2022.27645.1307ENAncy KandathilJosephChrist UniversityJoseph VargheseKureetharaChrist University0000-0001-5030-3948Journal Article20220120Suppose each edge of a simple connected undirected graph is given a unique number from the numbers $1, 2, \dots, $q$, where $q$ is the number of edges of that graph. Then each vertex is labelled with sum of the labels of the edges incident to it. If no two vertices have the same label, then the graph is called an antimagic graph. We prove that the Cartesian product of wheel graph and path graph is antimagic.http://comb-opt.azaruniv.ac.ir/article_14424_b9b8cdb8b1145b45090a1a3274f53ec7.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288420231231Independent Italian bondage of graphs6496641456810.22049/cco.2023.28662.1657ENSaeedKosariInstitute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China0000-0002-1427-5473JafarAmjadiAzarbaijan Shahid Madani University0000-0001-9340-4773AyshaKhanDepartment of Mathematics
Prince Sattam bin Abdulaziz University
Alkharj 11991, Saudi ArabiaLutzVolkmannRWTH Aachen University0000-0003-3496-277XJournal Article20230115An independent Italian dominating function (IID-function) on a graph $G$ is a function $f:V(G)\rightarrow\{0,1,2\}$ satisfying the conditions that (i) $\sum_{u\in N(v)}f(u)\geq2$ when $f(v)=0$, and (ii) the set of all vertices assigned non-zero values under $f$ is independent. The weight of an IID-function is the sum of its function values over all vertices, and the independent Italian domination number $i_{I}(G)$ of $G$ is the minimum weight of an IID-function on $G$. In this paper, we initiate the study of the independent Italian bondage number $b_{iI}(G)$ of a graph $G$ having at least one component of order at least three, defined as the smallest size of a set of edges of $G$ whose removal from $G$ increases $i_{I}(G)$. We show that the decision problem associated with the independent Italian bondage problem is NP-hard for arbitrary graphs. Moreover, various upper bounds on $b_{iI}(G)$ are established as well as exact values on it for some special graphs. In particular, for trees $T$ of order at least three, it is shown that $b_{iI}(T)\leq2$.http://comb-opt.azaruniv.ac.ir/article_14568_82a7c01d90c57f6a97ccd4fe7d740df1.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288420231231On signs of several Toeplitz--Hessenberg determinants whose elements contain central Delannoy numbers6656711443210.22049/cco.2022.27707.1324ENDa-WeiNiuDepartment of Science, Henan University of Animal Husbandry and Economy, Zhengzhou 450046,
Henan, China0000-0003-4033-7911Wen-HuiLiSchool of Economics, Technology and Media University of Henan Kaifeng, Henan, Kaifeng 475001,
China0000-0002-1848-8855FengQiInstitute of Mathematics, Henan Polytechnic University, Jiaozuo 454003, Henan, China0000-0001-6239-2968Journal Article20220228In the paper, by virtue of Wronski's formula and Kaluza's theorem for the power series and its reciprocal, and with the aid of the logarithmic convexity of a sequence constituted by central Delannoy numbers, the authors present negativity of several Toeplitz--Hessenberg determinants whose elements contain central Delannoy numbers and combinatorial numbers.http://comb-opt.azaruniv.ac.ir/article_14432_b3059b5a58ece757a87d60440c7e8f72.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288420231231Linear-time construction of floor plans for plane triangulations6736921442710.22049/cco.2022.27814.1361ENPinkiPinkiBits Pilani, Rajasthan0000-0001-8388-4216KrishnendraShekhawatDepartment of Mathematics, BITS Pilani, Pilani Campus, Rajasthan - 3330310000-0002-3408-7912Journal Article20220517This paper focuses on a novel approach for producing a floor plan (FP), either a rectangular (RFP) or an orthogonal (OFP) based on the concept of orthogonal drawings, which satisfies the adjacency relations given by any bi-connected plane triangulation $G$.<br /> Previous algorithms for constructing a FP are primarily restricted to the cases given below:<br /> \begin{enumerate}[(i)]<br /> \item A bi-connected plane triangulation without separating triangles (STs) and with at most 4 corner implying paths (CIPs), known as properly triangulated planar graph (PTPG).<br /> \item A bi-connected plane triangulation with an exterior face of length 3 and no CIPs, known as maximal planar graph (MPG).<br /> \end{enumerate}<br /> The FP obtained in the above two cases is a RFP or an OFP respectively. In this paper, we present the construction of a FP (RFP if exists, else an OFP), for a bi-connected plane triangulation $G$ in linear-time.http://comb-opt.azaruniv.ac.ir/article_14427_f48cecc39d5cde003158900a75a3e6c7.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288420231231On local antimagic chromatic number of various join graphs6937141442810.22049/cco.2022.27937.1399ENK.PremalathaKalasalingam Academy of Research and EducationGee-ChoonLauUniversiti Teknologi MARA,
Faculty of Computer
and Mathematical Sciences,
85100 Segamat,
Johor, MalaysiaSubramanianArumugamDirector (n-CARDMATH)
Kalasalingam University
Anand Nagar, Krishnankoil-626 126
Tamil Nadu, India0000-0002-4477-9453W.C.ShiuDepartment of Mathematics,
The Chinese University of Hong Kong,
Shatin, Hong Kong, P.R. China.Journal Article20220626A local antimagic edge labeling of a graph $G=(V,E)$ is a bijection $f:E\rightarrow\{1,2,\dots,|E|\}$ such that the induced vertex labeling $f^+:V\rightarrow \mathbb{Z}$ given by $f^+(u)=\sum f(e),$ where the summation runs over all edges $e$ incident to $u,$ has the property that any two adjacent vertices have distinct labels. A graph $G$ is said to be locally antimagic if it admits a local antimagic edge labeling. The local antimagic chromatic number $\chi_{la}(G)$ is the minimum number of distinct induced vertex labels over all local antimagic labelings of $G.$ In this paper we obtain sufficient conditions under which $\chi_{la}(G\vee H),$ where $H$ is either a cycle or the empty graph $O_n=\overline{K_n},$ satisfies a sharp upper bound. Using this we determine the value of $\chi_{la}(G\vee H)$ for many wheel related graphs $G.$http://comb-opt.azaruniv.ac.ir/article_14428_29f3bfe45780bf0345829025de1c755a.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288420231231Some properties of the essential annihilating-ideal graph of commutative rings7157241444810.22049/cco.2022.27827.1365ENMohdNazimDepartment of mathematics, Aligarh Muslim University, Aligarh.0000-0001-8817-4336Nadeem UrREHMANDepartment of Mathematics, Aligarh Muslim University, Aligarh-202002, IndiaShabir AhmadMirDepartment of Mathematics, Aligarh Muslim University, Aligarh-202002, India0000-0003-4743-6859Journal Article20220521Let $\mathcal{S}$ be a commutative ring with unity and $A(\mathcal{S})$ denotes the set of annihilating-ideals of $\mathcal{S}$. The essential annihilating-ideal graph of $\mathcal{S}$, denoted by $\mathcal{EG}(\mathcal{S})$, is an undirected graph with $A^*(\mathcal{S})$ as the set of vertices and for distinct $\mathcal{I}, \mathcal{J} \in A^*(\mathcal{S})$, $\mathcal{I} \sim \mathcal{J}$ is an edge if and only if $Ann(\mathcal{IJ}) \leq_e \mathcal{S}$. In this paper, we classify the Artinian rings $\mathcal{S}$ for which $\mathcal{EG}(\mathcal{S})$ is projective. We also discuss the coloring of $\mathcal{EG}(\mathcal{S})$. Moreover, we discuss the domination number of $\mathcal{EG}(\mathcal{S})$.http://comb-opt.azaruniv.ac.ir/article_14448_ba3e441a8980ace7b758bf37d6348917.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288420231231Cycle transit function and betweenness7257351443310.22049/cco.2022.27730.1332ENLekshmi KamalK SheelaDepartment of Futures Studies
University of Kerala
KaryavattomM.ChangatDepartment of Futures Studies
University of Kerala
Karyavattom
Trivandrum0000-0001-7257-6031AshaPailyDepartment of Futures Studies
University of Kerala
Karyavattom
TrivandrumJournal Article20220412Transit functions are introduced to study betweenness, intervals and convexity in an axiomatic setup on graphs and other discrete structures. Prime example of a transit function on graphs is the well studied interval function of a connected graph. In this paper, we study the Cycle transit function $\mathcal{C}( u,v)$ on graphs which is a transit function derived from the interval function. We study the betweenness properties and also characterize graphs in which the cycle transit function coincides with the interval function. We also characterize graphs where $|\mathcal{C}( u,v)\cap \mathcal{C}( v,w) \cap \mathcal{C}( u,w)|\le 1$ as an analogue of median graphs.http://comb-opt.azaruniv.ac.ir/article_14433_d2bf98b78a5a8de8e838fce06adc2ef2.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288420231231On several new closed-form evaluations for the generalized hypergeometric functions7377491443410.22049/cco.2022.27794.1355ENB. R. SrivatsaKumarDepartment of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher EducationDongkyuLimDepartment of Mathematics Education, Andong National UniversityArjun K.RathieVedant College of Engineering and Technology (Rajasthan Technical University)Journal Article20220504The main objective of this paper is to establish as many as thirty new closed-form evaluations of the generalized hypergeometric function $_{q+1}F_q(z)$ for $q= 2, 3$. This is achieved by means of separating the generalized hypergeometric function $_{q+1}F_q(z)$ for $q=1, 2, 3$ into even and odd components together with the use of several known infinite series involving reciprocal of the non-central binomial coefficients obtained earlier by L. Zhang and W. Ji.http://comb-opt.azaruniv.ac.ir/article_14434_3018f89e30d18f148883930c10790101.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288420231201Lower bound on the KG-Sombor index7517571458010.22049/cco.2023.28666.1662ENSaeedKosariInstitute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China0000-0002-1427-5473NasrinDehgardiDepartment of Mathematics and Computer Science, Sirjan University of TechnologyAyshaKhanDepartment of Mathematics
Prince Sattam bin Abdulaziz University
Alkharj 11991, Saudi ArabiaJournal Article20230107In 2021, a novel degree-based topological index was introduced by Gutman, called the Sombor index. Recently Kulli and Gutman introduced a vertex-edge variant of the Sombor index, is caled KG-Sombor index. In this paper, we establish lower bound on the KG-Sombor index and determine the extremal trees achieve this bound.http://comb-opt.azaruniv.ac.ir/article_14580_a22ab42da0fc4c7fe718e64e0e8e04f0.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288420231201Roman domination number of signed graphs7597661444310.22049/cco.2022.27733.1341ENJamesJosephCHRIST(Deemed to be University), Bangalore0000-0003-4685-4688MAYAMMAJOSEPHCHRIST(Deemed to be University) Hosur Road
Bangalore-5600290000-0001-5819-247XJournal Article20220402A function $f:V\rightarrow \{0,1,2\}$ on a signed graph $S=(G,\sigma)$ where $G = (V,E)$ is a Roman dominating function(RDF) if $f(N[v]) = f(v) + \sum_{u \in N(v)} \sigma(uv)f(u) \geq 1$ for all $v\in V$ and for each vertex $v$ with $f(v)=0$ there is a vertex $u$ in $N^+(v)$ such that $f(u) = 2$. The weight of an RDF $f$ is given by $\omega(f) =\sum_{v\in V}f(v)$ and the minimum weight among all the RDFs on $S$ is called the Roman domination number $\gamma_R(S)$. Any RDF on $S$ with the minimum weight is known as a $\gamma_R(S)$-function. In this article we obtain certain bounds for $ \gamma_{R} $ and characterise the signed graphs attaining small values for $ \gamma_R. $http://comb-opt.azaruniv.ac.ir/article_14443_47ff08fbefeb3ac814a397841975cbeb.pdf