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AVDTC Numbers of Generalized Halin Graphs with Maximum Degree at Least 6
作者姓名:Xiang-en  Chen  Zhong-fu  Zhang
作者单位:[1]College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, China [2]Institute of Applied Mathematics, Lanzhou Jiaotong University, Lanzhou, 730070, China
基金项目:Supported by the National Natural Science Foundation of China (No.10771091) and the Science and Research Project of the Education Department of Gansu Province (0501-02) and NWNU-KJCXGC-3-18.
摘    要:In a paper by Zhang and Chen et al.(see 11]), a conjecture was made concerning the minimum number of colors Xat(G) required in a proper total-coloring of G so that any two adjacent vertices have different color sets, where the color set of a vertex v is the set composed of the color of v and the colors incident to v. We find the exact values of Xat(G) and thus verify the conjecture when G is a Generalized Halin graph with maximum degree at least 6, A generalized Halin graph is a 2-connected plane graph G such that removing all the edges of the boundary of the exterior face of G (the degrees of the vertices in the boundary of exterior face of G are all three) gives a tree.

关 键 词:图论  广义Halin图  着色  AVDTC数
收稿时间:2005-12-15
修稿时间:2006-06-22

AVDTC numbers of generalized Halin graphs with maximum degree at least 6
Xiang-en Chen Zhong-fu Zhang.AVDTC Numbers of Generalized Halin Graphs with Maximum Degree at Least 6[J].Acta Mathematicae Applicatae Sinica,2008,24(1):55-58.
Authors:Xiang-en Chen  Zhong-fu Zhang
Institution:(1) College of Mathematics and Information Science, Northwest Normal University, Lanzhou, 730070, China;(2) Institute of Applied Mathematics, Lanzhou Jiaotong University, Lanzhou, 730070, China
Abstract:In a paper by Zhang and Chen et al.(see 11]), a conjecture was made concerning the minimum number of colors χ at (G) required in a proper total-coloring of G so that any two adjacent vertices have different color sets, where the color set of a vertex ν is the set composed of the color of ν and the colors incident to ν. We find the exact values of χ at (G) and thus verify the conjecture when G is a Generalized Halin graph with maximum degree at least 6. A generalized Halin graph is a 2-connected plane graph G such that removing all the edges of the boundary of the exterior face of G (the degrees of the vertices in the boundary of exterior face of G are all three) gives a tree. Supported by the National Natural Science Foundation of China (No.10771091) and the Science and Research Project of the Education Department of Gansu Province (0501-02) and NWNU-KJCXGC-3-18.
Keywords:Graph  total coloring  adjacent-vertex-distinguishing total coloring  adjacent-vertex-distinguishing total chromatic number  
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