| 摘要: |
| 本文研究了双圈图的邻点强可区别全染色问题,并利用结构分析法给出了双圈图的邻点强可区别全色数的上界. 即,当G是以∞-图为基图的双圈图时,则χast(G)≤△(G)+2;其他χast(G)≤△(G)+3.从而验证了张忠辅等提出的平面图的邻点强可区别全染色猜想在双圈图上是成立的. |
| 关键词: 双圈图 邻点强可区别全染色 邻点强可区别全色数 |
| DOI： |
| 分类号:O157.5 |
| 基金项目:国家自然科学基金资助项目(11961041,12261055); 甘肃省自然科学基金资助项目(21JR11RA065). |
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| ADJACENT VERTEX STRONGLY DISTINGUISHING TOTAL COLORING OF A BICYCLIC GRAPH |
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ZHOU Li1, WEN Fei1, LI Ze-peng2
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1.Institute of Applied Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China;2.School of Information Science and Engineering, Lanzhou University, Lanzhou 730030, China
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| Abstract: |
| In this paper, we consider the problem of adjacent vertex strongly distinguishable total coloring of a bicyclic graph. By using the structural analysis, the upper bound of the adjacent vertex strongly distinguishable total chromatic number of a bicyclic graph is given, that is, χast(G)≤△(G)+2 if G is a bicyclic graph with ∞-graph as its base graph; and χast(G)≤△(G)+3 otherwise. By the way, it further shows that the conjecture of adjacent vertex strongly distinguishable total coloring of a planer graph posed by Zhongfu Zhang et al. holds on bicyclic graphs. |
| Key words: bicyclic graph adjacent vertex strongly distinguishing total-coloring adjacent vertex strongly distinguishing total chromatic number |
