两类特殊图的邻点强可区别E-全染色  

On the adaject vertex strongly distinguishing E-total coloring of two special graphs

作　　者：顾忠栋 强会英[1] 魏邦魁 

机构地区：[1]兰州交通大学数理与软件工程学院,甘肃兰州730070

出　　处：《苏州科技学院学报（自然科学版）》2016年第3期18-21,共4页Journal of Suzhou University of Science and Technology （Natural Science Edition）

基　　金：国家自然科学基金资助项目(61262045)

摘　　要：对简单图G(V,E),存在一个正整数k,使得映射f:V(G)∪E(G)→{1,2,…,k},如果坌uv∈E(G),有f(u)≠f(v),f(u)≠f(uv)且C(u)≠C(v),其中C(u)={f(u)}∪{f(uv),f(v)|uv∈E(G),v∈V(G)},则称f是图G的邻点强可区别E-全染色,且称最小的数k为图G的邻点强可区别E-全色数。在此基础上应用构造染色法研究了图F_m×F_n、M(P_n^2)的邻点强可区别E-全染色,并得出了其邻点强可区别E-全色数。Let G （V,E） be a simple graph,k be a positive integer,f is a mapping from V（G）UE（G） to {1, 2,.-. ,k} ,thenf is called the adgacent vertex strongly distinguishing E-total coloring of G and the minimum number of k is called the adjacent vertex strongly distinguishing E-total chromatic of G, if uv ∈ E（G）f（u）≠f（v）, f（u） ≠f（uv）, uv ∈E（G）,C（u）≠C（v）. Based on this, this paper studied the adjacent vertex strongly distinguishing E-total coloring of graph of Fm×Fn and M（pn2） with the structure staining method. And the adjacent ver- tex strongly distinguishing E-total chromatic numbers of both graphs were obtained thereby.

关 键 词：笛卡尔积图 k方图 邻点强可区别E-全染色 邻点强可区别E-全色数 

分 类 号：O157.5[理学—数学]