关于一类联图的r-强边染色

The r-strong edge colorings of graphs on join graph

单图G的r-强边染色是指图的距离不超过r的任意两点可区别的边染色,所谓两点u,v间的距离是指这两个点之间的最短路的长,记为d(u,v).图G的r-强边色数χs′(G,r)表示.本文给出一类联图的2-强边色数的界,并将结论推广到r-强边色数的界.

Let G be a simple graph, for any u,v ∈ V（G） , d（u,v） denotes the distance between u and v. A proper edge coloring of a graph G is called an r - strong edge coloring if for any two distinct vertices u,v V（G） with d （ u, v） ≤ r, we have C （u） ≠ C （v） . The r - strong edge coloring number X＇s （ G, r） is the minimum number of colors required for an r - strong edge coloring of the graph G. In this paper, we obtain an upper bound for the 2 - strong edge coloring number of a kind of join graph. And we also discussed an upper bound for the r - strong edge coloring number.