一类图的邻点被扩展和可区别全染色  

Neighbor Expanded Sum and Distinguishing Total Coloring of Graphs

作　　者：贾甜夏 赵聪慧 张淑敏 JIA Tianxia;ZHAO Conghui;ZHANG Shumin(College of Mathematics and Statistics,Qinghai Normal University,Xining 810008,Qinghai;Academy of Plateau Science and Sustainability,Xining 810008,Qinghai)

机构地区：[1]青海师范大学数学与统计学院,青海西宁810008 [2]高原科学与可持续发展研究院,青海西宁810008

出　　处：《四川师范大学学报（自然科学版）》2023年第4期525-531,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(12261074、12201335和11661068);青海省科技厅项目(2021-ZJ-703)。

摘　　要：根据完全多部图的特点,得到完全三部图和完全四部图的邻点被扩展和可区别全色数≤2,并证明Flandrin等(Discussiones Mathematicae Graph Theory,2017,37(1):29-37.)提出的NESDTC猜想对于完全三部图和完全四部图成立.最后对完全多部图的NESD问题作部分研究.In this paper,we prove that the neighbor expanded sum and distinguishing total chromatic numbers of complete tripartite graphs and complete 4-partite graphs are no more than 2.This result illustrates that the NESDTC conjecture proposed by Flandrin et al(Discussiones Mathematicae Graph Theory,2017,37(1):29-37.)is true for complete tripartite graph and complete 4-partite graph.Moreover,the NESD problem of complete multipartite graph is partially studied.

关 键 词：完全三部图 完全四部图 完全多部图 邻点被扩展和可区别全染色 NESDTC猜想 

分 类 号：O157.5[理学—数学]