Upper Bounds on the D(β)-Vertex-Distinguishing Edge-Chromatic Numbers of Graphs

  • Authors:

  • Tian Jing-Jing;Liu Xin-Sheng;Zhang Zhong-Fu;Deng Fang-An

  • Affiliations:

  • Department of Mathematics, Shaanxi University of Technology, Hanzhong, Shaanxi 723001, China and College of Mathematics and Information Science, Northwest Normal University, Lanzhou, Gansu 730070, ...;Department of Mathematics, Shaanxi University of Technology, Hanzhong, Shaanxi 723001, China;Department of Mathematics, Shaanxi University of Technology, Hanzhong, Shaanxi 723001, China;Department of Mathematics, Shaanxi University of Technology, Hanzhong, Shaanxi 723001, China

  • Venue:
  • ICCS '07 Proceedings of the 7th international conference on Computational Science, Part III: ICCS 2007
  • Year:
  • 2007

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Abstract

In this paper, let d be the maximum degree of G, we study the upper bounds for the D(β)-vertex-distinguishing edge-chromatic number by probability method and prove that $$ \chi^\prime_{\beta-vd}(G)\leq \left\{ \begin{array}{ll} 2\sqrt{2(\beta-1)}d^{\frac{\beta+2}{2}},&\ \ d\geq 4, \beta \geq4;\\ 8d^{\frac{5}{2}},&\ \ d\geq 6, \beta=3;\\ 32d^2,&\ \ d\geq 4, \beta=2. \end{array}\right.$$