双圈图的邻点强可区别全染色  

ADJACENT VERTEX STRONGLY DISTINGUISHING TOTALCOLORING OF A BICYCLIC GRAPH

作　　者：周莉 文飞[1] 李泽鹏 ZHOU Lil;WEN Fei;LI Ze-peng(Institute of Applied Mathematics,Lanzhou Jiaotong University,Lanzhou 30070,China;School of Information Science and Engineering,Lanzhou University,Lanzhou 730030,China)

机构地区：[1]兰州交通大学应用数学研究所,甘肃兰州730070 [2]兰州大学信息科学与工程学院,甘肃兰州730030

出　　处：《数学杂志》2023年第6期537-546,共10页Journal of Mathematics

基　　金：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)。

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χ_(ast)(G)≤△(G)+2;其他χ_(ast)(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.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,X_(ast)(G)≤△(G)+2 if G isabicyclic graph with oo-graph asitsbasegraph;and X_(ast)(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.

关 键 词：双圈图 邻点强可区别全染色 邻点强可区别全色数 

分 类 号：O157.5[理学—数学]