关于若干倍图的第一类弱全染色

On a number of the first weak total coloring of double graphs

对简单图G(V,E),f是从V(G)∪E(G)到{1,2,…,k}的映射,k是自然数,如果对任意的uv∈E(G),有f(u)≠f(v),对任意的uv,uw∈E(G),v≠w,有f(uv)≠f(uw),则称f为图G的一个第一类弱全染色.最小的k称为G的第一类弱全色数.给出了路、圈、星、扇、轮、完全图的倍图的第一类弱全色数.

Let G be a simple graph,k is a positive integer.f is a mapping from V（G）∪E（G） to {1,2,…,k} such that  uv,uw∈E（G）,v≠w,f（uv）≠f（uw）,we say that f is the first weak total coloring of G.The minimal number of k is called the first weak total chromatic number of G.In this paper,we discuss the first weak total chromatic number of the double graph of path,circle,star,fan,wheel and complete.