S_n+W_n的邻点强可区别全色数

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.

On the Adjacent-Vertex-Strongly-Distinguishing Total Coloring of Sn+Wn

For any vertex u∈V(G),let TN={u}∪{uv|uv∈E(G),v∈V(G)}∪{v∈V(G)|uv∈E(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 Cf(u)={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(″avsdt″ is the abbreviation of ″adjacent-vertex-strongly-distinguishing total″).The avsdt-coloring of G,denoted by χast(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.