摘要
如果图G的一个正常全染色满足相邻点的色集合不同,且任意两种颜色所染的元素的数目之差的绝对值不超过1,则称为邻点可区别均匀全染色(AVDETC),其所用的最少颜色数称为邻点可区别均匀全色数。本文研究了路、圈、星、扇的Mycielski图的邻点可区别均匀全染色,利用构造法和匹配法给出了它们的邻点可区别全色数的确切值,验证了它们满足邻点可区别均匀全染色猜想(AVDETCC)。
A proper total coloring of graph G is called adjacent vertex-distinguishing-equitable( AVDETC),if adjacent vertices receive different color sets,and absolute values of the number of any two color classes differ by one. The required minimum number of colors is called the adjacent vertex-distinguishing-equitable total chromatic number. This paper gives adjacent vertex-distinguishing-equitable total coloring and adjacent vertex-distinguishing-equitable total chromatic number of Mycielski graphs of path,cycle,star and fan by using constructive method and matching method,which satisfies the conjecture on adjacent vertex-distinguishing-equitable total coloring( AVDETCC).
出处
《河南科技大学学报（自然科学版）》
CAS
北大核心
2013年第6期88-91,9,共4页
Journal of Henan University of Science And Technology:Natural Science
基金
中央高校基本科研业务费专项基金项目(2010LKSX06)
关键词
图论
MYCIELSKI图
邻点可区别均匀全染色
邻点可区别均匀全色数
graph theory
mycielski graph
adjacent vertex-distinguishing-equitable total coloring
adjacent vertex-distinguishing-equitable total chromatic number
