k-方图的邻点可区别无圈边染色

On the Adjacent Vertex-Distinguishing Acyclic Edge Coloring of k-th Power Graphs

图G的一个正常边染色被称作邻点可区别无圈边染色,如果G中无二色圈,且相邻点关联边的色集合不同.图G的邻点可区别无圈边色数记为χ′_^(aa)(G),即图G的一个邻点可区别无圈边染色所用的最少颜色数.通过构造具体染色的方法,给出了一些k-方图的邻点可区别无圈边色数.

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 to u is not equal to the coloring set of edges incident to v, where uv E E（G）. The adjacent Vertex-distinguishing acyclic edge chromatic number of G, denoted by Xaa,（G）, is the minimal number of colors in an adjacent vertex-distinguishing acyclic edge coloring of G. In this paper, we obtain adjacent vertex-distinguishing acyclic edge coloring of some k-th power graphs with construction method.