Journal of East China Normal University(Natural Sc ›› 2012, Vol. 2012 ›› Issue (5): 120-126.

• Article • Previous Articles     Next Articles

An upper bound for the vertex-distinguishing star edge chromatic number of graphs

LIU Xin-sheng, LU Wei-hua   

  1. College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, China
  • Received:2011-10-01 Revised:2012-02-01 Online:2012-09-25 Published:2012-09-29

Abstract: The vertex-distinguishing star edge chromatic number of $G$, denoted by $\chi'_{\rm vds}{(G)}$, is the minimum number of colors in a vertex-distinguishing star edge coloring of $G$. The vertex-distinguishing star edge colorings of some particular graphs were obtained. Furthermore, if $G(V,E)$ is a graph with $\delta\geqslant 5$, and $n\leqslant  \Delta^7$, then $\chi'_{\rm vds}{(G)}\leqslant 14\Delta^2$, where $n$ is the order of $G$,
$\delta(G)$ is the minimum degree of $G$, and $\Delta(G)$ is the maximum\linebreak degree of $G$.

Key words: vertex-distinguishing edge chromatic number, vertex-distinguishing star edge chromatic number, probability method

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