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. Copyright © 2011 Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer-Verlag Berlin Heidelberg.
Original language | English |
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Pages (from-to) | 439-452 |
Journal | Applied Mathematics |
Volume | 26 |
Issue number | 4 |
DOIs | |
Publication status | Published - Dec 2011 |
Citation
Shiu, W. C., Chan, W. H., Zhang, Z-F., & Bian, L. (2011). On the adjacent vertex-distinguishing acyclic edge coloring of some graphs. Applied Mathematics, 26(4), 439-452. doi: 10.1007/s11766-011-2309-2Keywords
- Adjacent strong edge coloring
- Adjacent vertex-distinguishing acyclic edge coloring