On the total liar's domination of graphs

Document Type : Original paper

Authors

1 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Shahid Rajaee Teacher Training University

Abstract

For a graph G, a set L of vertices is called a total liar's domination if |NG(u)L|2 for any uV(G) and |(NG(u)NG(v))L|3 for any distinct vertices u,vV(G). The total liar’s domination number is the cardinality of a minimum total liar’s
dominating set of G and is denoted by γTLR(G). In this paper we study the total liar's domination numbers of join and products of graphs.

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