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,若f满足(1)uv∈E(G),u≠v,f(u)≠f(v);(2)uv,uw∈E(G),v≠w,f(uv)≠f(uw);(3)uv∈E(G),C(u)≠C(v);其中C(u)={f(u)}∪{f(uv)|uv∈E(G)};则称f是G的一个关联邻点可区别全染色.给出了一类3-正则重圈图Re(n,m)(m≥2,n≥3且n≡0(mod2))的关联邻点可区别全色数.
Let G be a simple graph and k be a positive integer.If f is a mapping from V(G)∪E(G) to{1,2,…,k},such that(1)uv∈E(G),u≠v,f(u)≠f(v);(2)uv,vw∈E(G),u≠w,f(uv)≠f(vw);(3)uv∈E(G),C(u)≠C(v),we say that f is a incidence adjacent vertex-distinguishing total coloring of G,where C(u)={f(u)}∪{f(uv)|uv∈E(G)}.The minimal number of k is called as the incidence adjacent vertex-distinguishing total chromatic number of G.The incidence adjacent vertex-distinguishing total chromatic number of 3-repeated cycle graph is disussed.