Communications in Combinatorics and OptimizationCommunications in Combinatorics and Optimization
http://comb-opt.azaruniv.ac.ir/
Thu, 17 Aug 2017 14:08:03 +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.Wed, 31 May 2017 19:30:00 +0100Primal-dual path-following algorithms for circular programming
http://comb-opt.azaruniv.ac.ir/article_13631_0.html
Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case. Alizadeh and Goldfarb [Math. Program. Ser. A 95 (2003) 3-51] introduced primal-dual path-following algorithms for solving second-order cone programming problems. In this paper, we generalize their work by using the machinery of Euclidean Jordan algebras associated with the circular cones to derive primal-dual path-following interior point algorithms for circular programming problems. We prove polynomial convergence of the proposed algorithms by showing that the circular logarithmic barrier is a strongly self-concordant barrier. The numerical examples show the path-following algorithms are simple and efficient.Thu, 29 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.Wed, 31 May 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.Wed, 31 May 2017 19:30:00 +0100On leap Zagreb indices of graphs
http://comb-opt.azaruniv.ac.ir/article_13643_0.html
The first and second Zagreb indices of a graph are equal, respectively, to the sum of squares of the vertex degrees, and the sum of the products of the degrees of pairs of adjacent vertices. We now consider analogous graph invariants, based on the second degrees of vertices (number of their second neighbors), called leap Zagreb indices. A number of their basic properties is established.Sat, 08 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-connectedgraphsWed, 31 May 2017 19:30:00 +0100Some results on the complement of a new graph associated to a commutative ring
http://comb-opt.azaruniv.ac.ir/article_13644_0.html
The rings considered in this article are commutative with identity which are not fields. Let R be a ring. A. Alilou, J. Amjadi and Sheikholeslami introduced and investigated a graph whose vertex set is the set of all nontrivial ideals of R and distinct vertices I, J are joined by an edge in this graph if and only if either ann(I)J = (0) or ann(J)I = (0). They called this graph as a new graph associated to a commutative ring.Their above mentioned work appeared in the Journal, Discrete Mathematics Algorithms and Applications. The aim of this article is to investigate the interplay between some graph- theoretic properties of the complement of a new graph associated to a commutative ring R and the ring -theoretic-properties of R.Wed, 02 Aug 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 +0100Approximation Solutions for Time-Varying Shortest Path Problem
http://comb-opt.azaruniv.ac.ir/article_13645_0.html
Abstract. Time-varying network optimization problems have tradition-ally been solved by specialized algorithms. These algorithms have NP-complement time complexity. This paper considers the time-varying short-est path problem, in which can be optimally solved in O(T(m + n)) time,where T is a given integer. For this problem with arbitrary waiting times,we propose an approximation algorithm, which can solve the problem withO(T(m+n)/ k ) time complexity such that evaluates only a subset of the valuesfor t = {0, 1, . . . , T}.Thu, 10 Aug 2017 19:30:00 +0100On the signed Roman edge k-domination in graphs
http://comb-opt.azaruniv.ac.ir/article_13642_2227.html
Let $kgeq 1$ be an integer, and $G=(V,E)$ be a finite and simplegraph. The closed neighborhood $N_G[e]$ of an edge $e$ in a graph$G$ is the set consisting of $e$ and all edges having a commonend-vertex with $e$. A signed Roman edge $k$-dominating function(SREkDF) on a graph $G$ is a function $f:E rightarrow{-1,1,2}$ satisfying the conditions that (i) for every edge $e$of $G$, $sum _{xin N[e]} f(x)geq k$ and (ii) every edge $e$for which $f(e)=-1$ is adjacent to at least one edge $e'$ forwhich $f(e')=2$. The minimum of the values $sum_{ein E}f(e)$,taken over all signed Roman edge $k$-dominating functions $f$ of$G$, is called the signed Roman edge $k$-domination number of $G$and is denoted by $gamma'_{sRk}(G)$. In this paper we establish some new bounds on the signed Roman edge $k$-domination number.Wed, 31 May 2017 19:30:00 +0100