若干Mycielski图的邻点可区别均匀全染色  

Adjacent Vertex-distinguishing-equitable Total Coloring of Mycielski Graphs

作　　者：史小艺[1] 苗连英[1] 张宁[1] 

机构地区：[1]中国矿业大学理学院,江苏徐州221008

出　　处：《河南科技大学学报（自然科学版）》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)

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).

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 

分 类 号：O157.5[理学—数学]