# 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 $|N_G(u)\cap L|\geq 2$ for any $u\in V(G)$ and $|(N_G(u)\cup N_G(v))\cap L|\geq 3$ for any distinct vertices $u,v\in V(G)$. The total liar’s domination number is the cardinality of a minimum total liar’s
dominating set of $G$ and is denoted by $\gamma_{TLR}(G)$. In this paper we study the total liar's domination numbers of join and products of graphs.

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Main Subjects

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