若干多重联图的邻点可区别E-全染色

Adjacent Vertex-distinguishing E-total Coloring on the Multiple Join Graph of the San and Simple Graph

G(V,E)是一个简单图,k是一个正整数,f是一个V(G)∪E(G)到{1,2,…,k}的映射.如果uv∈E(G),则f(u)≠f(v),f(u)≠f(uv),f(v)≠f(uv),C(u)≠C(v),称f是图G的邻点可区别E-全染色,称最小的数k为图G的邻点可区别E-全色数.本文给出了扇与星、路、圈间的多重联图的邻点可区别E-全色数.其中C(u)={f(u)}∪{f(uv)|uv∈E(G)}.

Let G（V,E） be a simple graph,k be a positive integer,f be a mapping from V（G） ∪E（G） to {1, 2,…,k}. If arbitary uv∈E（G）,we have f（u）≠f（v）,f（u）≠f（uv）,f（v）≠f（uv）,C（u）≠C（v）. Then f is called the adjacent vertex-distinguishing E-number of G. The minimal number or k is called the adjacent vertex-distinguishing E-total chromatic number of G. The adjacent vertex-distinguishing E-total chromatic number of the multiple join graph of fan, star,path and cycle is obtained in the paper,where C（u）= {f（u）} ∪ {f （uv） ｜ uv∈ E（G） }.