摘要
对简单图 G(V,E) ,V(Gk) =V(G) ,E(Gk ) =E(G)∪ { uv|d(u,v) =k} ,称 Gk为 G的 k次方图 ,其中d (u,v)表示 u,v在 G中的距离 .设 f为用 k色时 G的正常全染色法 ,对 uv∈ E(G) ,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 为 G的 k邻点可区别的强全染色法 ,简记作 k- ASVDTC,且称 χast(G) =min{ k|k- ASVDTC of G}为 G的邻点可区别的强全色数 .本文得到了 k≡2 (mod3)时的 χast(Pkn) ,其中 Pn 为 n阶路 .
Let G(V,E) be a simple graph,V(G k)=V(G),E(G k)=E(G)∪{uv|d(u,v)=k},G k is called a k-power graph of G,where d(u,v) is denoted the distance from u to v. Suppose f is a proper total coloring of G which use k colors,for uv∈E(G), it's satisfied C(u)≠C(v),where C(u)={f(u)}∪{f(v)|uv∈E(G)}∪{f(uv)|uv∈E(G)}, then f is called a k adjacent strong vertex-distinguishing total coloring of graph G(k-ASVDTC for short)and χ ast (G)=min{k|k-ASVDTC of G} is called the chromatic number of adjacent strong vertex-distinguishing total coloring of graph G. In this paper,we get the X ast (P k n) of P k n(k≡2 (mod 3)),where P n be a path of order n.
出处
《经济数学》
2003年第4期77-80,共4页
Journal of Quantitative Economics
关键词
强全染色
邻点可区别
简单图
临强边染色
k-power graph of path,total coloring, adjacent strong vertex-distinguishing total coloring
