S_n+W_n的邻点强可区别全色数  

On the Adjacent-Vertex-Strongly-Distinguishing Total Coloring of S_n+W_n

作　　者：王树勋[1] 

机构地区：[1]陕西理工学院数学系,陕西汉中723001

出　　处：《数学的实践与认识》2008年第18期229-232,共4页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10771091);陕西省教育厅基金(07JK209)

摘　　要：设G(V,E)是阶数不小于3的简单连通图,k是自然数,f是从V(G)∪E(G)到1,2,…,k的映射,满足:对任意的uv∈E(G),f(u)≠f(v),f(u)≠f(uv)≠f(v);对任意的uv,uw∈E(G)(v≠w),f(uv)≠f(uw);对任意的uv∈E(G),C(u)≠C(v),其中C(u)={f(u)}∪{f(v)uv∈E(G)}∪{f(uv)uv∈E(G)},则称f是图G的一个邻点强可区别的全染色法,简记作k-AVSDTC,且称χast(G)=min{k G的所有k-AVSDTC}为G的邻点强可区别的全色数.得到了星与轮联图的邻点强可区别的全色数.For any vertex u∈V（G）,let Tn={u}∪{uv｜uv∈E（G）,v∈V（G）}∪{v∈V（G）｜ and let f be a total k- coloring of G. The total-color neighbor of a vertex u of G is the color set C（u）7={f（x）｜x∈TN（u）}. For any two adjacent vertices x and y of V（G） such that Cf（x） ≠Cf（y）, we refer to f as a k avsdt-coloring of G C＂avsdt＂ is the abbreviation of ＂adjacent vertex-strongly-distinguishing total＂）. The avsdt coloring of G, denoted by Zast, （G）, is the minimal number of colors required for a avsdt-coloring of G. In this paper, we have obtained the adjacent-vertex strong distinguishing total chromatic number of Sn ＋ Wn

关 键 词：星 轮 联图 邻点强可区别全色数 

分 类 号：O157.5[理学—数学] O156.1[理学—基础数学]