On the independence transversal total domination number of graphs

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• 作者：Abel Cabrera Martí ; nez^a ; José ; M. Sigarreta Almira^a ; Ismael G. Yero^b ; ^{ismael.gonzalez@uca.es}
• 关键词：Independence transversal total domination number ; Total domination number ; Independence number
• 刊名：Discrete Applied Mathematics
• 出版年：2017
• 出版时间：11 March 2017
• 年：2017
• 卷：219
• 期：Complete
• 页码：65-73
• 全文大小：434 K
• 卷排序：219

文摘

A total dominating set of a graph GG having non empty intersection with all the independent sets of maximum cardinality in GG is an independent transversal total dominating set. The minimum cardinality of any independent transversal total dominating set is denoted by γtt(G)γtt(G). In this paper we introduce this concept and begin the study of its mathematical properties. Specifically, we prove that the complexity of the decision problem associated to the computation of the value of γtt(G)γtt(G) is NP-complete, under the assumption that the independence number is known. Moreover, we present tight lower and upper bounds on γtt(G)γtt(G) and give some realizability results in concordance with these bounds. For instance, we show that for any two positive integers a,ba,b such that 2≤a≤2b3 there is a graph GG of order bb such that γtt(G)=aγtt(G)=a.