On the adjacent vertex-distinguishing acyclic edge coloring of some graphs |
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Authors: | Wai Chee Shiu Wai Hong Chan Zhong-fu Zhang Liang Bian |
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Affiliation: | 1.Department of Mathematics,Hong Kong Baptist University,Kowloon Tong, Hong Kong,China;2.Institute of Applied Mathematics,Lanzhou Jiaotong University,Lanzhou,China |
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Abstract: | A proper 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 coloring set of edges incident with u is not equal to the coloring set of edges incident with v, where uv ∈ E(G). The adjacent vertex distinguishing acyclic edge chromatic number of G, denoted by x′ Aa (G), is the minimal number of colors in an adjacent vertex distinguishing acyclic edge coloring of G. If a graph G has an adjacent vertex distinguishing acyclic edge coloring, then G is called adjacent vertex distinguishing acyclic. In this paper, we obtain adjacent vertex-distinguishing acyclic edge coloring of some graphs and put forward some conjectures. |
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Keywords: | Adjacent strong edge coloring adjacent vertex-distinguishing acyclic edge coloring. |
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