Results 21 to 30 of about 5,516,987 (160)
Edge-Distinguishing Index of a Graph [PDF]
Graphs and Combinatorics, 2014 We introduce a concept of edge-distinguishing colourings of graphs. A closed neighbourhood of an edge $${e\in E(G)}$$e∈E(G) is a subgraph N[e] induced by e and all edges adjacent to it.
R. Kalinowski, M. Woźniak
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On the Total-Neighbor-Distinguishing Index by Sums [PDF]
Graphs and Combinatorics, 2015 We consider a proper coloring c of edges and vertices in a simple graph and the sum f(v) of colors of all the edges incident to v and the color of a vertex v.
M. Pilsniak, M. Woźniak
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Distinguishing number and distinguishing index of neighbourhood corona of two graphs [PDF]
Contributions to Discrete Mathematics, 2016 The distinguishing number (index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling (edge labeling) with $d$ labels that is preserved only by a trivial automorphism.
S. Alikhani, S. Soltani
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Distinguishing index of graphs with simple automorphism groups
European Journal of Combinatorics, 2022 The distinguishing index \(D^\prime (\Gamma)\) of a graph \(\Gamma\) is the least number \(d\) such that \(\Gamma\) has an edge-coloring with \(d\) colors preserved only by the trivial automorphism. This definition was introduced by \textit{R. Kalinowski} and \textit{M. Pilśniak} [Eur. J. Comb. 45, 124--131 (2015; Zbl 1304.05046)]. The analogous notion
Mariusz Grech, A. Kisielewicz
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Distinguishing number and distinguishing index of some operations on graphs [PDF]
Journal of Information and Optimization Sciences, 2016 The distinguishing number (index) D(G) (Dʹ(G)) of a graph G is the least integer d such that G has an vertex labeling (edge labeling) with d labels that is preserved only by a trivial automorphism.
S. Alikhani, S. Soltani
semanticscholar +3 more sources
پژوهشهای ریاضی, 2020 Introduction The graph is a mathematical model for a discrete set whose members are interlinked in some way. The members of this collection can be the different parts of the earth and the connections between them are bridges that tie them together (like ...
Saeid Alikhani, Samaneh Soltani
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The distinguishing index of the Cartesian product of finite graphs
Ars Mathematica Contemporanea, 2016 The distinguishing index D ʹ( G ) of a graph G is the least natural number d such that G has an edge colouring with d colours that is only preserved by the identity automorphism.
Aleksandra Gorzkowska +2 more
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On the Neighbor Sum Distinguishing Index of Planar Graphs [PDF]
CoRR, 2014 Let c be a proper edge coloring of a graph G=(V,E) with integers 1,2,…,k . Then k≥Δ(G) , while Vizing's theorem guarantees that we can take k≤Δ(G)+1 .
Marthe Bonamy, J. Przybylo
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The distinguishing index of the Cartesian product of countable graphs
Ars Mathematica Contemporanea, 2016 The distinguishing index D ′ ( G ) of a graph G is the least cardinal d such that G has an edge colouring with d colours that is preserved only by the trivial automorphism. We derive some bounds for this parameter for infinite graphs.
I. Broere, M. Pilsniak
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The distinguishing index of graphs with infinite minimum degree [PDF]
Journal of Graph Theory, 2022 The distinguishing index D′(G) $D^{\prime} (G)$ of a graph G $G$ is the least number of colors necessary to obtain an edge coloring of G $G$ that is preserved only by the trivial automorphism.
Marcin Stawiski, T. Wilson
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