Communications in Combinatorics and OptimizationCommunications in Combinatorics and Optimization
http://comb-opt.azaruniv.ac.ir/
Thu, 29 Jun 2017 11:49:56 +0100FeedCreatorCommunications in Combinatorics and Optimization
http://comb-opt.azaruniv.ac.ir/
Feed provided by Communications in Combinatorics and Optimization. Click to visit.The locating-chromatic number for Halin graphs
http://comb-opt.azaruniv.ac.ir/article_13577_2227.html
Let G be a connected graph. Let f be a proper k -coloring of G and Π = (R_1, R_2, . . . , R_k) bean ordered partition of V (G) into color classes. For any vertex v of G, define the color code c_Π(v) of v with respect to Π to be a k -tuple (d(v, R_1), d(v, R_2), . . . , d(v, R_k)), where d(v, R_i) is the min{d(v, x)|x ∈ R_i}. If distinct vertices have distinct color codes, then we call f a locating coloringof G. The locating-chromatic number of G, denoted by χL(G), is the least number k such that Gadmits a locating coloring with k colors. In this paper, we determine the locating-chromatic numberof Halin graphs. We also give the locating-chromatic number of Halin graphs of double stars.Fri, 30 Jun 2017 19:30:00 +0100On net-Laplacian Energy of Signed Graphs
http://comb-opt.azaruniv.ac.ir/article_13578_2227.html
A signed graph is a graph where the edges are assigned either positive ornegative signs. Net degree of a signed graph is the dierence between the number ofpositive and negative edges incident with a vertex. It is said to be net-regular if all itsvertices have the same net-degree. Laplacian energy of a signed graph is defined asε(L(Σ)) =|γ_1-(2m)/n|+...+|γ_n-(2m)/n| where γ_1,...,γ_n are the eigenvalues of L(Σ) and (2m)/n isthe average degree of the vertices in Σ. In this paper, we dene net-Laplacian matrixconsidering the edge signs of a signed graph and give bounds for signed net-Laplacianeigenvalues. Further, we introduce net-Laplacian energy of a signed graph and establishnet-Laplacian energy bounds.Fri, 30 Jun 2017 19:30:00 +0100Reformulated F-index of graph operations
http://comb-opt.azaruniv.ac.ir/article_13630_0.html
The first general Zagreb index is defined as $M_1^lambda(G)=sum_{vin V(G)}d_{G}(v)^lambda$. The case $lambda=3$, is called F-index. Similarly, reformulated first general Zagreb index is defined in terms of edge-drees as $EM_1^lambda(G)=sum_{ein E(G)}d_{G}(e)^lambda$ and the reformulated F-index is $RF(G)=sum_{ein E(G)}d_{G}(e)^3$. In this paper, we compute the reformulated F-index for some graph operations.Fri, 23 Jun 2017 19:30:00 +0100On global (strong) defensive alliances in some product graphs
http://comb-opt.azaruniv.ac.ir/article_13595_2227.html
A defensive alliance in a graph is a set $S$ of vertices with the property that every vertex in $S$ has at most one moreneighbor outside of $S$ than it has inside of $S$. A defensive alliance $S$ is called global if it forms a dominating set. The global defensive alliance number of a graph $G$ is the minimum cardinality of a global defensive alliance in $G$. In this article we study the global defensive alliances in Cartesian product graphs, strong product graphs and direct product graphs. Specifically we give several bounds for the global defensive alliance number of these graph products and express them in terms of the global defensive alliance numbers of the factor graphs.Sun, 30 Jul 2017 19:30:00 +0100Sufficient conditions for maximally edge-connected and super-edge-connected
http://comb-opt.azaruniv.ac.ir/article_13594_2227.html
Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximallyedge-connected or super-edge-connected if the numberof edges is large enough. Examples will demonstrate that our conditions are sharp.noindent {bf Keywords:} Edge-connectivity; Maximally edge-connected graphs; Super-edge-connectedgraphsFri, 30 Jun 2017 19:30:00 +0100Peripheral Wiener Index of a Graph
http://comb-opt.azaruniv.ac.ir/article_13596_2227.html
The eccentricity of a vertex $v$ is the maximum distance between $v$ and anyother vertex. A vertex with maximum eccentricity is called a peripheral vertex.The peripheral Wiener index $ PW(G)$ of a graph $G$ is defined as the sum ofthe distances between all pairs of peripheral vertices of $G.$ In this paper, weinitiate the study of the peripheral Wiener index and we investigate its basicproperties. In particular, we determine the peripheral Wiener index of thecartesian product of two graphs and trees.Wed, 31 May 2017 19:30:00 +0100