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    20 results
    Ebrahim Vatandoost, Masoumeh Khalili
    Journal article | Electronic Journal of Graph Theory and Applications ยท 2018 | ๐Ÿ‡ฌ๐Ÿ‡ง English
    Let G be a non-abelian group. The non-commuting graph of group G, shown by ฮ“G, is a graph with the vertex set G \ Z(G), where Z(G) is the center of group G. Also two distinct vertices of a and b are a...
    Sarah-Marie Belcastro
    Journal article | Electronic Journal of Graph Theory and Applications ยท 2018 | ๐Ÿ‡ฌ๐Ÿ‡ง English
    We correct a small error in a 1996 paper of Albertson and Haas, and extend their lower bound for the fraction of properly colorable edges of planar subcubic graphs that are simple, connected, bridgele...
    Ju Zhou
    Journal article | Electronic Journal of Graph Theory and Applications ยท 2018 | ๐Ÿ‡ฌ๐Ÿ‡ง English
    A graph G is perfect matching transitive, shortly PM-transitive, if for any two perfect matchings M and N of G, there is an automorphism fโ€„:โ€„V(G)โ€„โ†ฆโ€„V(G) such that fe(M)โ€„=โ€„N, where fe(uv)โ€„=โ€„f(u)f(v). I...
    Martin Baca, Muhammad Irfan, Aisha Javed, Andrea Semanicova-Fenovcikova
    Journal article | Electronic Journal of Graph Theory and Applications ยท 2018 | ๐Ÿ‡ฌ๐Ÿ‡ง English
    For a simple graph Gโ€„=โ€„(V,โ€†E) this paper deals with the existence of an edge labeling ฯ†โ€„:โ€„E(G)โ€„โ†’โ€„{0,โ€†1,โ€†โ€ฆ,โ€†kโ€…โˆ’โ€…1}, 2โ€„โ‰คโ€„kโ€„โ‰คโ€„โˆฃE(G)โˆฃ, which induces a vertex labeling ฯ†โ€…*โ€…โ€„:โ€„V(G)โ€„โ†’โ€„{0,โ€†1,โ€†โ€ฆ,โ€†kโ€…โˆ’โ€…1} in suc...
    Diamantis Koreas
    Journal article | Electronic Journal of Graph Theory and Applications ยท 2018 | ๐Ÿ‡ฌ๐Ÿ‡ง English
    V.G. Vizing showed that any graph belongs to one of two classes: Class 1 if ฯ‡สน(G)โ€„=โ€„ฮ”(G) or in class 2 if ฯ‡สน(G)โ€„=โ€„ฮ”(G)โ€…+โ€…1, where ฯ‡สน(G) and ฮ”(G) denote the edge chromatic index of G and the maximum de...
    S. Susilawati, Edy Tri Baskoro, Rinovia Simanjuntak
    Journal article | Electronic Journal of Graph Theory and Applications ยท 2018 | ๐Ÿ‡ฌ๐Ÿ‡ง English
    In 2010, Nurdin, Baskoro, Salman and Gaos conjectured that the total vertex irregularity strength of any tree T is determined only by the number of vertices of degrees 1, 2 and 3 in T. This paper will...
    Hafizh M. Radiapradana, Suhadi Wido Saputro, Erma Suwastika, Oki Neswan, Andrea Semanicova-Fenovcฤฑkova
    Journal article | Electronic Journal of Graph Theory and Applications ยท 2018 | ๐Ÿ‡ฌ๐Ÿ‡ง English
    For integer kโ€„โ‰ฅโ€„2, let Xโ€„=โ€„{0,โ€†1,โ€†2,โ€†โ€ฆ,โ€†k}. In this paper, we determine the order of a star graph K1,โ€†n of nโ€…+โ€…1 vertices, such that K1,โ€†n admits a topological integer additive set-labeling (TIASL) wi...
    Chithra Mr, Manju K. Menon, A. Vijayakumar
    Journal article | Electronic Journal of Graph Theory and Applications ยท 2018 | ๐Ÿ‡ฌ๐Ÿ‡ง English
    Many graphs such as hypercubes, star graphs, pancake graphs, grid, torus etc are known to be good interconnection network topologies. In any network topology, the vertices represent the processors and...
    Leomarich F. Casinillo
    Journal article | Electronic Journal of Graph Theory and Applications ยท 2018 | ๐Ÿ‡ฌ๐Ÿ‡ง English
    Let G = (V(G), E(G)) be a path of order n โ‰ฅ 1. Let fm(G) be a path with m โ‰ฅ 0 independent dominating vertices which follows a Fibonacci string of binary numbers where 1 is the dominating vertex. A set...
    Dalibor Froncek, Aaron Shepanik
    Journal article | Electronic Journal of Graph Theory and Applications ยท 2018 | ๐Ÿ‡ฌ๐Ÿ‡ง English
    A handicap distance antimagic labeling of a graph G = (V, E) with n vertices is a bijection fฬ‚ : V โ†’ {1, 2, โ€ฆ, n} with the property that fฬ‚(xi) = i, the weight w(xi) is the sum of labels of all neighb...
    Christina Eubanks-Turner, Aihua Li
    Journal article | Electronic Journal of Graph Theory and Applications ยท 2018 | ๐Ÿ‡ฌ๐Ÿ‡ง English
    In this paper, we study the interlace polynomials of friendship graphs, that is, graphs that satisfy the Friendship Theorem given by Erdรถs, Rรฉnyi and Sos. Explicit formulas, special values and behavio...
    Abdollah Alhevaz, Maryam Baghipur, Ebrahim Hashemi
    Journal article | Electronic Journal of Graph Theory and Applications ยท 2018 | ๐Ÿ‡ฌ๐Ÿ‡ง English
    The distance signless Laplacian spectral radius of a connected graph G is the largest eigenvalue of the distance signless Laplacian matrix of Gโ€Ž, โ€Ždefined as โ€ŽDโ€ŽQ(G)โ€„=โ€„Tr(G)โ€…+โ€…D(G)โ€Ž, โ€Žwhere D(G) is th...
    Cristina Dalfo, Miquel ร€ngel Fiol
    Journal article | Electronic Journal of Graph Theory and Applications ยท 2018 | ๐Ÿ‡ฌ๐Ÿ‡ง English
    A graph is a mathematical object modeling the existence of a certain relation between pairs of elements of a given set. Many of the first results concerning graphs made reference to relationships betw...
    Fendy Septyanto, Kiki A. Sugeng
    Journal article | Electronic Journal of Graph Theory and Applications ยท 2018 | ๐Ÿ‡ฌ๐Ÿ‡ง English
    Let G be a graph with an edge k-coloring ฮณ : E(G) โ†’ {1, โ€ฆ, k} (not necessarily proper). A path is called a rainbow path if all of its edges have different colors. The map ฮณ is called a rainbow colorin...
    Suresh Elumalai, Toufik Mansour, Mohammad Ali Rostami
    Journal article | Electronic Journal of Graph Theory and Applications ยท 2018 | ๐Ÿ‡ฌ๐Ÿ‡ง English
    The hyper-Zagreb index of a simple connected graph G is defined by ${\chi ^2}(G) = \sum_{uv \in E(G)} {{{\left( {d(u) + d(v)} \right)}^2}}$. In this paper, we establish, analyze and compare some new u...
    Vladimir Dimitrov Samodivkin
    Journal article | Electronic Journal of Graph Theory and Applications ยท 2018 | ๐Ÿ‡ฌ๐Ÿ‡ง English
    The bondage number b(G) of a graph G is the smallest number of edges whose removal from G results in a graph with larger domination number. We obtain sufficient conditions for the validity of the ineq...
    Luis R. Fuentes, Italo J. Dejter, Carlos A. Araujo
    Journal article | Electronic Journal of Graph Theory and Applications ยท 2018 | ๐Ÿ‡ฌ๐Ÿ‡ง English
    Let $0<n\in\mathbb{Z}$. In the unit distance graph of $\mathbb{Z}^n\subset\mathbb{R}^n$, a perfect dominating set is understood as having induced components not necessarily trivial. A modification ...
    Sudip Bera
    Journal article | Electronic Journal of Graph Theory and Applications ยท 2018 | ๐Ÿ‡ฌ๐Ÿ‡ง English
    Given a group G, the intersection power graph of G, denoted by $\mathcal{G}_I(G)$, is the graph with vertex set G and two distinct vertices x and y are adjacent in $\mathcal{G}_I(G)$ if there exists ...