若干倍图的邻点可区别的I-均匀全染色  

Incidence-adjacent Vertex Distinguishing Equitable Total Coloring of Some Double Graphs

作　　者：张婷 朱恩强 赵慧霞 Zhang Ting;Zhu Enqiang;Zhao Huixia(Normal School, Lanzhou University of Arts and Science, Lanzhou 730010, China;Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China;Journal Editorial Department, Lanzhou University of Arts and Science, Lanzhou 730010, China)

机构地区：[1]兰州文理学院教育学院,甘肃兰州730000 [2]广州大学计算机科技研究院,广东广州510006 [3]兰州文理学院学报编辑部,甘肃兰州730000

出　　处：《宁夏大学学报（自然科学版）》2020年第3期237-240,245,共5页Journal of Ningxia University(Natural Science Edition)

基　　金：甘肃省高等学校创新能力提升项目(2019B-195);国家自然科学基金资助项目(61872101)。

摘　　要：对图G的一个邻点可区别的I-全染色f,若f还满足任意两种颜色所染元素(点和边)个数最大相差为1,则称f为图G的一个邻点可区别的I-均匀全染色.对图G进行邻点可区别的I-均匀全染色所需最少的颜色数称为图G的邻点可区别I-均匀全色数.研究了图D(Cn),D(Sn),D(Fn),D(Wn)的邻点可区别I-均匀全染色,通过函数构造法,得到了其的邻点可区别I-均匀全色数,并验证了其满足猜想:χaet^i(G)≤Δ(G)+2.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 satisfy the maximum difference in the number of elements(vertex or edge)dyed by any two colors is one.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 G.In this paper,we have obtained the incidence-adjacent vertex distinguishing equitable total chromatic number of D(Cn),D(Sn),D(Fn),D(Wn)by function construction methods,which meet the suspect:χaet^i(G)≤Δ(G)+2.

关 键 词：倍图 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]