Adjacent vertex distinguishing colorings by sum of sparse graphs

作者：Yu, Xiaowei; Qu, Cunquan; Wang, Guanghui^*; Wang, Yiqiao

来源：Discrete Mathematics, 2016, 339(1): 62-71.

DOI：10.1016/j.disc.2015.07.011

• Proper edge coloring
• Neighbor sum distinguishing edge coloring
• Maximum average degree
• Combinatorial Nullstellensatz

A neighbor sum distinguishing edge-k-coloring, or nsd-k-coloring for short, of a graph G is a proper edge coloring of G with elements from {1, 2,..., k} such that no pair of adjacent vertices meets the same sum of colors of G. The definition of this coloring makes sense for graphs containing no isolated edges (we call such graphs normal). Let mad(G) and Delta(G) be the maximum average degree and the maximum degree of a graph G, respectively. In this paper, we prove that every normal graph with Delta(G) >= 5 and mad(G) < 3 admits an nsd-(Delta(G) + 2)-coloring. Our approach is based on the Combinatorial Nullstellensatz and the discharging method.

• 出版日期2016-1-6
• 单位北京中医药大学; 中国科学院数学与系统科学研究院; 山东大学