星扇轮联图的邻点可约边染色

对简单图G(V,E),若存在自然数κ(1≤κ≤Δ(G))和映射f:E(G)→{1,2,…,κ}使得对任意相邻两点u,v∈V(G),uv∈E(G),当d(u)=d(v)时,有C(u)=C(u),则f为G的κ-邻点可约边染色(简记为κ-AVREC of G),而x′_(aur)(G)=max{κ|κ-AVREC of G}称为G的邻点可约边染色数.其中C(u)={f(uv)|uv∈E(G)}.证明了联图在若干情况下的邻点可约边染色定理,得到了S_n+S_n,F_n+F_n,W_n+W_n,S_n+F_n,S_n+W_n和F_n+W_n的邻点可约边色数.

Adjacent Reducible Edge Cloring of Star Fan Wheel of Join-Graphs

Let G be a simple graph,k is a positive integer.f is a mapping from E(G) to {1,2,…,k},such that∨uv,uw∈E(G),d(u) = d(v);a.nd c(u) = c(v),then f is callled the k adjacent reducible edge aloring of G.Which is abbreviated by K-AVREC of G,and X’avr(G) = max{k|k—AVRECofG} is called the adjacent reducible edge chromatic number of G.In this paper,we have proved theorems of adjacent reducible coloring of some circumstances, and adjacent reducble edge chromatic number of some join-graphs(S_n + S_n,F_n + F_n,W_n + W_nS_n + F_n,S_n + W_n,F_n + W_n) is obtained.