D(p_n)图的邻点强可区别全染色

Adjacent Strong Verte-Distinuishing Total Coloring of D(p_n)

设f为用k色时G的正常全染色法,对任意的边uv∈E(G),其端点的色集合满足C(u)≠C(v),其中C(u)={f(u)}∪{f(v)|uv∈E(G)}∪{f(uv)|uv∈E(G)},则称f是G的k邻点强可区别的全染色法(简记作k-AVSDTC),且称ast(G)=min{k|G的所有k-AVSDTC}为G的邻点强可区别全色数.本文得到D(pn)图的邻点强可区别全色数,其中pn为n阶路.

Suppose f is a proper total coloring of G which use k colors, for any uv∈E（G） ,it＇s satisfied C（u）≠C（v） ,where C（u={f（u））U{f（v）｜uv∈E（G））U{f（uv）}uv∈E（G））, then f is call a adjacent strong vertex-distinguishing total coloring of graph G and xast （G）= = min{k }k-AVSDTC of G} is called the chromatic number of adjacent strong vertex-distinguishing total coloring of graph G. In this paper we get the xast（D（pn））, where pn be a path of order n.