路和圈多重联图的邻点可区别E-全染色

Adjacent vertex-distinguishing E-total coloring on the multiple join graphs of path and circle

设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u,v∈E(G),则f(u)=f(v),f(u)=f(uv),f(v)=f(uv),C(u)=C(v),其中C(u)={f(u)}∪{f(uv)|uv∈E(G)}.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.讨论了路和圈的多重联图的邻点可区别E-全色数。

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 uv ∈ E（G）,we have f（u） = f（v）,f（u） = f（uv）,f（v） = f（uv）,C（u） = C（v）,where C（u） = {f（u）} ∪ {f（uv）｜uv ∈ E（G）}.Then f is called the adjacent vertex-distinguishing E-total coloring.The minimal number of 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 path and circle are obtained in this paper.