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 ci be the number of edges colored by i. If [...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 ci be the number of edges colored by i. If [ci - cj] ≤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.展开更多
基金Supported by the Fundamental Research Funds for the Central Universities(Grant Nos. 2011B019)the National Natural Science Foundation of China (Grant Nos. 10971144+2 种基金1110102011171026)the Natural Science Foundation of Beijing (Grant No. 1102015)
文摘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 ci be the number of edges colored by i. If [ci - cj] ≤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.
基金国家"九七三"重点基础研究发展规划项目基金(2006CB303005)国家自然科学基金(60903016+4 种基金6053311060773063)新世纪优秀人才支持计划(NCET-05-0333)黑龙江省教育厅科学技术研究项目(11531276)NSFC-RGC of China(60831160525)资助~~
