Adjacent Vertex Distinguishing Proper Edge Colorings of Bicyclic Graphs

An adjacent vertex distinguishing proper edge coloring of a graph G is a proper edge coloring of G such that no pair of adjacent vertices meets the same set of colors. Let x'a(G) be the minimum number of colors required to give G an adjacent vertex distinguishing proper edge coloring. In this p...

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Published inIAENG international journal of applied mathematics Vol. 48; no. 4; pp. 1 - 11
Main Authors Chen, Xiang'en, Liu, Shunyi
Format Journal Article
LanguageEnglish
Published Hong Kong International Association of Engineers 01.11.2018
Subjects
Apexes
Graph coloring
Graph theory
Graphs
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Abstract An adjacent vertex distinguishing proper edge coloring of a graph G is a proper edge coloring of G such that no pair of adjacent vertices meets the same set of colors. Let x'a(G) be the minimum number of colors required to give G an adjacent vertex distinguishing proper edge coloring. In this paper, we show that x'a(G) < A(G) + 1 for bicyclic graphs G, where A(G) is the maximum degree of G.
AbstractList An adjacent vertex distinguishing proper edge coloring of a graph G is a proper edge coloring of G such that no pair of adjacent vertices meets the same set of colors. Let x'a(G) be the minimum number of colors required to give G an adjacent vertex distinguishing proper edge coloring. In this paper, we show that x'a(G) < A(G) + 1 for bicyclic graphs G, where A(G) is the maximum degree of G.
Author Chen, Xiang'en
Liu, Shunyi
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SubjectTerms Apexes
Graph coloring
Graph theory
Graphs
Title Adjacent Vertex Distinguishing Proper Edge Colorings of Bicyclic Graphs
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