路与路联图的邻强边染色和均匀邻强边染色(英文)

Adjacent strong edge coloring and equitable adjacent strong edge coloring of the joins of paths

对于图G的一个正常边染色c,如果相邻的点所关联的边集的色集不相等,c称为邻强边染色.图G的邻强边染色所需要的最小值称为图G的邻强边色数.如果每个色类所含的边数最多差一,c被称为均匀边染色,其最小值称为图G的均匀边色数.论文确定了路与路联图的邻强边染色数和均匀邻强边染色数.

For a proper edge coloring c of a graph G, if the sets of colors of adjacent vertices are distinct, the edge coloring c is called an adjacent strong edge coloring of G. Let c-1 （i） be the set of edges that are colored by i, if ｜｜ c-1 （i） - c- （j） ｜｜≤ 1 for any two colors i andj ,then c is an equitable edge coloring of G. The coloring c is an equitable adjacent strong edge coloring of G , if it is both adjacent strong edge coloring and equitable adjacent strong edge coloring. The least number of colors of such a coloring c is called the equitable adjacent strong edge chromatic index of G. In this paper, we obtained the adjacent strong edge chromatic index and the equitable adjacent strong edge chromatic index of the joins of paths.