2012•Journal of Northwest University for NationalitiesRequires access

The vertex-distinguishing equitable acyclic edge-coloring of some Mycielski's Graphs

Sun Xiang-tao

Abstract

A vertex-distinguishing edge coloring σ of a simple graph G is called vertex disti-nguishing equitable acyclic edge-coloring, if there are no bichromatic cycles in G, and ||Ei-|Ej||≤1,which Ei is edge sets with i color, then i=1,2,…, k. The smallest number k of colors is called thevertex-distinguishing equitable acyclic chromatic index ofG. In this paper, the vertex-distinguishingequitable acyclic edge-coloring of the Mycielski' graphs of some graphs with △(G)=2 are studied andobtained the exact values.

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Key concepts: Combinatorics, Edge coloring, Mathematics, Vertex (graph theory), Directed acyclic graph, Complete coloring, Brooks' theorem, Discrete mathematics