标题：ON THE TOTAL RESTRAINED DOMINATION NUMBER OF DIRECT PRODUCTS OF GRAPHS
作者：Shiu, Wai Chee; Chen, Hong-Yu; Chen, Xue-Gang; Sun, Pak Kiu
作者机构：[Shiu, Wai Chee; Sun, Pak Kiu] Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China.; [Chen, Hong-Yu] Shandong Univ, Sch Math 更多
通讯作者地址：[Shiu, WC]Hong Kong Baptist Univ, Dept Math, 224 Waterloo Rd, Kowloon Tong, Hong Kong, Peoples R China.
来源：DISCUSSIONES MATHEMATICAE GRAPH THEORY
关键词：total domination number; total restrained domination number; direct; product of graphs
摘要：Let G = (V, E) be a graph. A total restrained dominating set is a set S subset of V where every vertex in V \ S is adjacent to a vertex in S as well as to another vertex in V \ S, and every vertex in S is adjacent to another vertex in S. The total restrained domination number of G, denoted by gamma(t)(r)(G), is the smallest cardinality of a total restrained dominating set of G. We determine lower and upper bounds on the total restrained domination number of the direct product of two graphs. Also, we show that these bounds are sharp by presenting some infinite families of graphs that attain these bounds.