积图邻强边色数的注记

A Note of Adjacent Strong Edge Chromatic Number of Product Graphs

给出了积图邻强边色数的两个定理.在此基础上,证明了:对积图T×Wm,T×Fm和T×Sm,当T的最大度点不相邻时,它们的邻强边色数均为Δ(T)+m.当T的最大度点相邻时,它们的邻强边色数均为Δ(T)+m+1.其中T为n(n≥3)阶树图.Wm,Fm与Sm分别为m+1(m≥4)阶的轮,扇和星图.

In this paper,two theorem about the adjacent strong edge chromatic number of product graphs are given.Based on this,it has been proved that for the three product praphs T×W_m,T×F_m and T×S_m,if any two vertices of maximum degree are not adjacent in tree T,the adjacent strong edge chromatic number of these product graphs are all Δ(T)+m.When T has two vertices of maximum degree which are adjacent,the adjacent strong edge chromatic number of these product graphs are all Δ(T)+m+1.T is tree graph with n(n≥3) order.W_m,F_m and S_m are wheel,fan and star graphs with m+1(m≥4) order,respectively.