Equitable Strong Edge Coloring of the Joins of Paths and Cycles

DOI：10.3770/j.issn:2095-2651.2012.01.002

 作者 单位 王涛 华北科技学院基础部, 河北 三河 065201 刘明菊 北京航空航天大学数学系, 北京 100083 李德明 首都师范大学数学系, 北京 100048

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.本文确定了路与圈图的联图有均匀邻强边染色所需要的颜色数的最小值即均匀邻强边色数.

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_i\$ be the number of edges colored by \$i\$. If \$|c_i-c_j|\le 1\$ for any two colors \$i\$ and \$j\$, 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 edge coloring. The least number of colors of such a coloring \$c\$ is called the equitable adjacent strong chromatic index of \$G\$. In this paper, we determine the equitable adjacent strong chromatic index of the joins of paths and cycles. Precisely, we show that the equitable adjacent strong chromatic index of the joins of paths and cycles is equal to the maximum degree plus one or two.