Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288320230901Normalized distance Laplacian matrices for signed graphs4454561439110.22049/cco.2022.27514.1282ENROSHNI TROYRESEARCH SCHOLAR
DEPARTMENT OF MATHEMATICS
CENTRAL UNIVERSITY OF KERALA
KASARAGOD, INDIA0000-0001-6232-1086GerminaK ACentral University of Kerala, Kasaragod, India0000-0002-2643-3416Shahul HameedKAssociate Professor, Department of Mathematics, K M M Government Women's College, Kannur, India.Journal Article20211114In this paper, we introduce the notion of normalized distance Laplacian matrices for signed graphs corresponding to the two signed distances defined for signed graphs. We characterize balance in signed graphs using these matrices and compare the normalized distance Laplacian spectral radius of signed graphs with that of all-negative signed graphs. Also we characterize the signed graphs having maximum normalized distance Laplacian spectral radius.http://comb-opt.azaruniv.ac.ir/article_14391_c66c8a9abab76abb8f61f607986a6b5a.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288320230901Signed total Italian domination in digraphs4574661440810.22049/cco.2022.27700.1318ENLutzVolkmannRWTH Aachen University0000-0003-3496-277XJournal Article20220225Let $D$ be a finite and simple digraph with vertex set $V(D)$. A signed total Italian dominating function (STIDF) on a digraph $D$ is a function $f:V(D)\rightarrow\{-1,1,2\}$ satisfying the conditions that (i) $\sum_{x\in N^-(v)}f(x)\ge 1$ for each $v\in V(D)$, where $N^-(v)$ consists of all vertices of $D$ from which arcs go into $v$, and (ii) every vertex $u$ for which $f(u)=-1$ has an in-neighbor $v$ for which $f(v)=2$ or two in-neighbors $w$ and $z$ with $f(w)=f(z)=1$. The weight of an STIDF $f$ is $\sum_{v\in V(D)}f(v)$. The signed total Italian domination number $\gamma_{stI}(D)$ of $D$ is the minimum weight of an STIDF on $D$. In this paper we initiate the study of the signed total Italian domination number of digraphs, and we present different bounds on $\gamma_{stI}(D)$. In addition, we determine the signed total Italian domination number of some classes of digraphs.http://comb-opt.azaruniv.ac.ir/article_14408_17d0e8e2890d7e5de888e48b939c4e2e.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288320230901Weak Roman domination stable graphs upon edge-addition4674811441010.22049/cco.2022.27765.1348ENRoushini LeelyPushpamUniversity of MadrasNAGARAJANSRILAKSHMIDEPARTMENT OF MATHEMATICS
DHANRAJ BAID JAIN COLLEGEJournal Article20220411A Roman dominating function (RDF) on a graph $G$ is a function $f: V(G) \to \{0, 1, 2\}$ such that every vertex with label 0 has a neighbor with label 2. A vertex $u$ with $f(u)=0$ is said to be undefended if it is not adjacent to a vertex with $f(v)>0$. The function $f:V(G) \to \{0, 1, 2\}$ is a weak Roman dominating function (WRDF) if each vertex $u$ with $f(u) = 0$ is adjacent to a vertex $v$ with $f(v) > 0$ such that the function $f^{\prime}: V(G) \to \{0, 1, 2\}$ defined by $f^{\prime}(u) = 1$, $f^{\prime}(v) = f(v) - 1$ and $f^{\prime}(w) = f(w)$ if $w \in V - \{u, v\}$, has no undefended vertex. A graph $G$ is said to be Roman domination stable upon edge addition, or just $\gamma_R$-EA-stable, if $\gamma_R(G+e)= \gamma_R(G)$ for any edge $e \notin E(G)$. We extend this concept to a weak Roman dominating function as follows: A graph $G$ is said to be weak Roman domination stable upon edge addition, or just $\gamma_r$-EA-stable, if $\gamma_r(G+e)= \gamma_r(G)$ for any edge $e \notin E(G)$. In this paper, we study $\gamma_r$-EA-stable graphs, obtain bounds for $\gamma_r$-EA-stable graphs and characterize $\gamma_r$-EA-stable trees which attain the bound. http://comb-opt.azaruniv.ac.ir/article_14410_5980e502155f4b53abf564175b8a4474.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288320230901On the Total Monophonic Number of a Graph4834891441910.22049/cco.2022.27731.1331ENSubramanianArumugamDirector (n-CARDMATH)
Kalasalingam University
Anand Nagar, Krishnankoil-626 126
Tamil Nadu, India0000-0002-4477-9453SanthakumaranA.P.Department of Mathematics
Hindustan Institute of Technology and Science
Chennai - 603 103, IndiaTitusP.Department of Mathematics, University College of Engineering, NagercoilGanesamoorthyK.Department of Mathematics, Coimbatore Institute of Technology
(Government Aided Autonomous Institution)
Coimbatore - 641 014, IndiaMuruganM.Mathematics, Coimbatore Institute of Technology, Coimbatore - 14Journal Article20220327Let G = (V,E) be a connected graph of order n. A path P in G which does not have a chord is called a monophonic path. A subset S of V is called a monophonic set if every vertex v in V lies in a x-y monophonic path where x, y 2 S. If further the induced subgraph G[S] has no isolated vertices, then S is called a total monophonic set. The total monophonic number mt(G) and the upper total monophonic number m+t (G) are respectively the minimum cardinality of a total monophonic set and the maximum cardinality of a minimal total monophonic set. In this paper we determine the value of these parameters for some classes of graphs and establish bounds for the same. We also prove the existence of graphs with prescribed values for mt(G) and m+t (G).http://comb-opt.azaruniv.ac.ir/article_14419_3b612b136058ece9bbe77e34c11e4fb0.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288320230901Double Roman domination in graphs: algorithmic complexity4915031442510.22049/cco.2022.27661.1309ENAbolfazlPoureidiShahrood University of TechnologyJournal Article20220131Let $G=(V,E)$ be a graph. A double Roman dominating function (DRDF) of $G $ is a function $f:V\to \{0,1,2,3\}$ such that, for each $v\in V$ with $f(v)=0$, there is a vertex $u $ adjacent to $v$ with $f(u)=3$ or there are vertices $x$ and $y $ adjacent to $v$ such that $f(x)=f(y)=2$ and for each $v\in V$ with $f(v)=1$, there is a vertex $u $ adjacent to $v$ with $f(u)>1$. The weight of a DRDF $f$ is $ f (V) =\sum_{ v\in V} f (v)$. Let $n$ and $k$ be integers such that $3\leq 2k+ 1 \leq n$. The generalized Petersen graph $GP (n, k)=(V,E) $ is the graph with $V=\{u_1, u_2,\ldots, u_n\}\cup\{v_1, v_2,\ldots, v_n\}$ and $E=\{u_iu_{i+1}, u_iv_i, v_iv_{i+k}: 1 \leq i \leq n\}$, where addition is taken modulo $n$. In this paper, we firstly prove that the decision problem associated with double Roman domination is NP-omplete even restricted to planar bipartite graphs with maximum degree at most 4. Next, we give a dynamic programming algorithm for computing a minimum DRDF (i.e., a DRDF with minimum weight along all DRDFs) of $GP(n,k )$ in $O(n81^k)$ time and space and so a minimum DRDF of $GP(n,O(1))$ can be computed in $O( n)$ time and space.http://comb-opt.azaruniv.ac.ir/article_14425_f71d8f6209980c6952292d6281ceb02d.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288320230901An upper bound on triple Roman domination5055111442110.22049/cco.2022.27816.1359ENM.HajjariAzarbaijan Shahid Madani UniversityHosseinAbdollahzadeh AhangarBabol Noshirvani University of Technology0000-0002-0038-8047RanaKhoeilarAzarbaijan Shahid Madani University0000-0002-2981-3625ZehuiShaoGuangzhou University0000-0003-0764-4135S.M.SheikholeslamiAzarbaijan Shahid Madani University0000-0003-2298-4744Journal Article20220416For a graph $G=(V,E)$, a triple Roman dominating function (3RD-function) is a function $f:V\to \{0,1,2,3,4\}$ having the property that (i) if $f(v)=0$ then $v$ must have either one neighbor $u$ with $f(u)=4$, or two neighbors $u,w$ with $f(u)+f(w)\ge 5$ or three neighbors $u,w,z$ with $f(u)=f(w)=f(z)=2$, (ii) if $f(v)=1$ then $v$ must have one neighbor $u$ with $f(u)\ge 3$ or two neighbors $u,w$ with $f(u)=f(w)=2$, and (iii) if $f(v)=2$ then $v$ must have one neighbor $u$ with $f(u)\ge 2$. The weight of a 3RDF $f$ is the sum $f(V)=\sum_{v\in V} f(v)$, and the minimum weight of a 3RD-function on $G$ is the triple Roman domination number of $G$, denoted by $\gamma_{[3R]}(G)$. In this paper, we prove that for any connected graph $G$ of order $n$ with minimum degree at least two, $\gamma_{[3R]}(G)\leq \frac{3n}{2}$.http://comb-opt.azaruniv.ac.ir/article_14421_05e32ae64375bfd597ea59eef02b9e9d.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288320230901On Sombor coindex of graphs5135291442210.22049/cco.2022.27751.1343ENChinglensanaPhanjoubamMathematics Department,
North Eastern Hill University
Shillong India0000-0003-1975-2635Sainkupar MarweinMawiongDepartment of Basic Sciences and Social Sciences, North Eastern Hill University,
Mawlai Umshing, Shillong, Meghalaya, India Pin code - 7930220000-0002-3552-4408Ardeline MBuhphangDepartment of Mathematics, North Eastern Hill University
Shillong IndiaJournal Article20220405In this paper, we explore several properties of Sombor coindex of a finite simple graph and we derive a bound for the total Sombor index. We also explore its relations to the Sombor index, the Zagreb coindices, forgotten coindex and other important graph parameters. We further compute the bounds of the Somber coindex of some graph operations and derived explicit formulae of Sombor coindex for some well-known graphs as application.http://comb-opt.azaruniv.ac.ir/article_14422_d678ce7d8f0a8a8daf85442d27c853e6.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288320230901A homogeneous predictor-corrector algorithm for stochastic nonsymmetric convex conic optimization with discrete support5315591442910.22049/cco.2022.27449.1266ENBahaAlzalgDepartment of Mathematics,
The University of Jordan.0000-0002-1839-8083MohammadAlabedalhadiMath Dept, Balqa Applied UniversityJournal Article20211006We consider a stochastic convex optimization problem over nonsymmetric cones with discrete support. This class of optimization problems has not been studied yet. By using a logarithmically homogeneous self-concordant barrier function, we present a homogeneous predictor-corrector interior-point algorithm for solving stochastic nonsymmetric conic optimization problems. We also derive an iteration bound for the proposed algorithm. Our main result is that we uniquely combine a nonsymmetric algorithm with efficient methods for computing the predictor and corrector directions. Finally, we describe a realistic application and present computational results for instances of the stochastic facility location problem formulated as a stochastic nonsymmetric convex conic optimization problem.http://comb-opt.azaruniv.ac.ir/article_14429_0fbdc3396bab022b9b1e59d06fe7b586.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288320230901Signless Laplacian eigenvalues of the zero divisor graph associated to finite commutative ring $ \mathbb{Z}_{p^{M_{1}}q^{M_{2}}} $5615741442310.22049/cco.2022.27783.1353ENShariefuddinPirzadaDepartment of Mathematics, HazratbalBilalRatherUniversity of Kashmir0000-0003-1381-0291Rezwan UlShabanDepartment of Mathematics, University of KashmirTariqChishtiUniversity of KashmirJournal Article20220427For a commutative ring $R$ with identity $1\neq 0$, let the set $Z(R)$ denote the set of zero-ivisors and let $Z^{*}(R)=Z(R)\setminus \{0\}$ be the set of non-zero zero-divisors of $R$. The zero-divisor graph of $R$, denoted by $\Gamma(R)$, is a simple graph whose vertex set is $Z^{*} (R)$ and two vertices $u, v \in Z^*(R)$ are adjacent if and only if $uv=vu=0$. In this article, we find the signless Laplacian spectrum of the zero divisor graphs $ \Gamma(\mathbb{Z}_{n}) $ for $ n=p^{M_{1}}q^{M_{2}}$, where $ p<q $ are primes and $ M_{1} , M_{2} $ are positive integers.http://comb-opt.azaruniv.ac.ir/article_14423_bb4de937deddf13539bf65ceb1ee53d4.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288320230901Total restrained Roman domination5755871442610.22049/cco.2022.27628.1303ENJafarAmjadiAzarbaijan Shahid Madani University0000-0001-9340-4773BabakSamadiFaculty of Mathematical Sciences, Alzahra University, Tehran, IranLutzVolkmannRWTH Aachen University0000-0003-3496-277XJournal Article20220114Let $G$ be a graph with vertex set $V(G)$. A Roman dominating function (RDF) on a graph $G$ is a function $f:V(G)\longrightarrow\{0,1,2\}$ such that every vertex $v$ with $f(v)=0$ is adjacent to a vertex $u$ with $f(u)=2$. If $f$ is an RDF on $G$, then let $V_i=\{v\in V(G): f(v)=i\}$ for $i\in\{0,1,2\}$. An RDF $f$ is called a restrained (total) Roman dominating function if the subgraph induced by $V_0$ (induced by $V_1\cup V_2$) has no isolated vertex. A total and restrained Roman dominating function is a total restrained Roman dominating function. The total restrained Roman domination number $\gamma_{trR}(G)$ on a graph $G$ is the minimum weight of a total restrained Roman dominating function on the graph $G$. We initiate the study of total restrained Roman domination number and present several sharp bounds on $\gamma_{trR}G)$. In addition, we determine this parameter for some classes of graphs.http://comb-opt.azaruniv.ac.ir/article_14426_d5f2a14f23334b09e3f71e675a41e54c.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288320230901A note on odd facial total-coloring of cacti5895941445810.22049/cco.2022.27895.1388ENJuliusCzapDepartment of Applied Mathematics and Business Informatics, Faculty of Economics, Technical University of Kosice0000-0002-9933-5884Journal Article20220622A facial total-coloring of a plane graph $G$ is a coloring of the vertices and edges such that no facially adjacent edges, no adjacent vertices, and no edge and its endvertices are assigned the same color. A facial total-coloring of $G$ is odd if for every face $f$ and every color $c$, either no element or an odd number of elements incident with $f$ is colored by $c$. In this note we prove that every cactus forest with an outerplane embedding admits an odd facial total-coloring with at most 16 colors. Moreover, this bound is tight.http://comb-opt.azaruniv.ac.ir/article_14458_5845ed2278653c2ca1ef0b462e225152.pdfAzarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288320230901Face-magic labelings of some gridded graphs5956011453410.22049/cco.2023.28208.1478ENBryanFreybergUniversity of Minnesota Duluth, Duluth, MN, USAJournal Article20230101A type $(1,1,1)$ face-magic labeling of a planar graph $G=(V,E,F)$ is a bijection from $V\cup E \cup F$ to the set of labels $\{1,2,\dots,|V|+|E|+|F|\}$ such that the weight of every $n$-sided face of $G$ is equal to the same fixed constant. The weight of a face $\mathcal{F} \in F$ is equal to the sum of the labels of the vertices, edges, and face that determine $\mathcal{F}$. It is known that the grid graph $P_m \square P_n$ admits a type $(1,1,1)$ face-magic labeling, but the proof in the literature is quite lengthy. We give a simple proof of this result and show two more infinite families of gridded graphs admit type $(1,1,1)$ face-magic labelings.http://comb-opt.azaruniv.ac.ir/article_14534_f19a08449df334c4053dbae6c266d05e.pdf