若干Mycielski图邻点可区别Ⅰ-均匀全染色  

Incidence-adjacent vertex distinguishing equitable total coloring of some Mycielski graphs

作　　者：张婷[1] 朱恩强[2] 赵双柱 杜佳 ZHANG Ting;ZHU Enqiang;ZHAO Shuangzhu;DU Jia(Normal School,Lanzhou University of Arts and Science,Lanzhou 730000,China;School of Electronics Engineering and Computer Science,Peking University,Beijing 100871,China;School of Digital Media,Lanzhou University of Arts and Science,Lanzhou 730000,China)

机构地区：[1]兰州文理学院师范学院,甘肃兰州730000 [2]北京大学信息科学技术学院,北京100871 [3]兰州文理学院数字媒体学院,甘肃兰州730000

出　　处：《大连理工大学学报》2018年第5期547-550,共4页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(60974112);中国博士后科学基金资助项目(2015M580928)

摘　　要：图G的一个邻点可区别Ⅰ-均匀全染色是指对图G的邻点可区别的一个Ⅰ-全染色f,若f还满足||T_i|-|T_j||≤1(i≠j),其中T_i=V_i∪E_i={v|v∈V(G),f(v)=i}∪{e|e∈E(G),f(e)=i},则称f为图G的一个邻点可区别Ⅰ-均匀全染色,而图G的邻点可区别Ⅰ-均匀全染色中所用的最少颜色数称为图G的邻点可区别Ⅰ-均匀全色数.通过函数构造法,得到了M(Pn)、M(Cn)、M(Sn)的邻点可区别Ⅰ-均匀全色数,并且满足猜想.The incidence-adjacent vertex distinguishing equitable total coloring of graph G is that to the incidence-adjacent vertex distinguishing total coloring f of graph G,if f satisfies T i-T j≤1(i≠j),where T i=V i∪E i={v v∈V(G),f(v)=i}∪{e e∈E(G),f(e)=i},then f is called the incidence-adjacent vertex distinguishing equitable total coloring of graph G.The minimum number of colors required in incidence-adjacent vertex distinguishing equitable total coloring is called incidence-adjacent vertex distinguishing equitable total chromatic number of graph G.The incidence-adjacent vertex distinguishing equitable total chromatic numbers of M(P n),M(C n),M(S n)are obtained by function construction methods,which meet the suspect.

关 键 词：MYCIELSKI图 邻点可区别Ⅰ-均匀全染色 邻点可区别Ⅰ-均匀全色数 

分 类 号：O157.5[理学—数学]