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An upper bound for the adjacent vertex distinguishing acyclic edge chromatic number of a graph

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Abstract

A proper k-edge coloring of a graph G is called adjacent vertex distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the color set of edges incident to u is not equal to the color set of edges incident to υ, where uυ ∈ E(G). The adjacent vertex distinguishing acyclic edge chromatic number of G, denoted by χ′ aa (G), is the minimal number of colors in an adjacent vertex distinguishing acyclic edge coloring of G. In this paper we prove that if G(V, E) is a graph with no isolated edges, then χ′ aa (G) ≤ 32Δ.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Northwest Normal University, Lanzhou, 730070, China

    Xin-sheng Liu & Yang Gao

  2. Tianjin University of Science and Technology, Tianjin, 300222, China

    Ming-qiang An

Authors
  1. Xin-sheng Liu
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  2. Ming-qiang An
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  3. Yang Gao
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Correspondence to Xin-sheng Liu.

Additional information

Supported by the Natural Science Foundation of Gansu Province (3ZS051-A25-025)

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Liu, Xs., An, Mq. & Gao, Y. An upper bound for the adjacent vertex distinguishing acyclic edge chromatic number of a graph. Acta Math. Appl. Sin. Engl. Ser. 25, 137–140 (2009). https://doi.org/10.1007/s10255-007-7020-y

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  • DOI: https://doi.org/10.1007/s10255-007-7020-y

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