The locating-chromatic number for Halin graphs I.A. Purwasih Institut Teknologi Bandung author Edy T. Baskoro Institut Teknologi Bandung author H. Assiyatun Institut Teknologi Bandung author D. Suprijanto Institut Teknologi Bandung author M. Baca Technical University in Koˇsice author text article 2017 eng 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. Communications in Combinatorics and Optimization Azarbaijan Shahid Madani University 2538-2128 2 v. 1 no. 2017 1 9 http://comb-opt.azaruniv.ac.ir/article_13577_c74fa5dbcdcae6f2d922402512b3e4bc.pdf dx.doi.org/10.22049/cco.2017.13577 On net-Laplacian Energy of Signed Graphs Nutan Nayak S.S.Dempo College of Commerce and Economics, Altinho, Panaji,Goa author text article 2017 eng A signed graph is a graph where the edges are assigned either positive ornegative signs. Net degree of a signed graph is the di erence 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 defi ned 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 de ne 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. Communications in Combinatorics and Optimization Azarbaijan Shahid Madani University 2538-2128 2 v. 1 no. 2017 11 19 http://comb-opt.azaruniv.ac.ir/article_13578_948f7678fc0070ff67068a94731b67f8.pdf dx.doi.org/10.22049/cco.2017.13578 On global (strong) defensive alliances in some product graphs Ismael Gonzalez Yero University of Cadiz author Marko Jakovac University of Maribor author Dorota Kuziak Universitat Rovira i Virgili author text article 2017 eng 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. Communications in Combinatorics and Optimization Azarbaijan Shahid Madani University 2538-2128 2 v. 1 no. 2017 21 33 http://comb-opt.azaruniv.ac.ir/article_13595_d725af4d472f1574e07ceddb207995cf.pdf dx.doi.org/10.22049/cco.2017.13595 Sufficient conditions for maximally edge-connected and super-edge-connected Lutz Volkmann RWTH Aachen University author Zhen-Mu Hong Anhui University of Finance and Economics author text article 2017 eng 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-connectedgraphs Communications in Combinatorics and Optimization Azarbaijan Shahid Madani University 2538-2128 2 v. 1 no. 2017 35 41 http://comb-opt.azaruniv.ac.ir/article_13594_f13dab4717cdbf819f2dae83f101834a.pdf dx.doi.org/10.22049/cco.2017.13594 Peripheral Wiener Index of a Graph Kishori Narayankar Mangalore University author Lokesh B Mangalore University author text article 2017 eng 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. Communications in Combinatorics and Optimization Azarbaijan Shahid Madani University 2538-2128 2 v. 1 no. 2017 43 56 http://comb-opt.azaruniv.ac.ir/article_13596_983abceb15410e89528e5fcbb919dade.pdf dx.doi.org/10.22049/cco.2017.13596 On the signed Roman edge k-domination in graphs Akram Mahmoodi Department of Mathematics Payame Noor University I.R. Iran author text article 2017 eng 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. Communications in Combinatorics and Optimization Azarbaijan Shahid Madani University 2538-2128 2 v. 1 no. 2017 57 64 http://comb-opt.azaruniv.ac.ir/article_13642_c8b75d7b7cce416e2210ba5e68bb4ee2.pdf dx.doi.org/10.22049/cco.2017.25962.1061