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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In memory of the third author Prof. ZHANG Zhong-fu (1937–July 16, 2010)
This work is partially supported by NSFC of China (No. 19871036 and No. 40301037) and Faculty Research Grant, Hong Kong Baptist University.
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Shiu, W.C., Chan, W.H., Zhang, Zf. et al. On the adjacent vertex-distinguishing acyclic edge coloring of some graphs. Appl. Math. J. Chin. Univ. 26, 439–452 (2011). https://doi.org/10.1007/s11766-011-2309-2
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DOI: https://doi.org/10.1007/s11766-011-2309-2