Revista de la
Unión Matemática Argentina
The total co-independent domination number of some graph operations
Abel Cabrera Martínez, Suitberto Cabrera García, Iztok Peterin, and Ismael G. Yero
Volume 63, no. 1 (2022), pp. 153–168    

https://doi.org/10.33044/revuma.1652

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Abstract

A set $D$ of vertices of a graph $G$ is a total dominating set if every vertex of $G$ is adjacent to at least one vertex of $D$. The total dominating set $D$ is called a total co-independent dominating set if the subgraph induced by $V(G) - D$ is edgeless. The minimum cardinality among all total co-independent dominating sets of $G$ is the total co-independent domination number of $G$. In this article we study the total co-independent domination number of the join, strong, lexicographic, direct and rooted products of graphs.