The total co-independent domination number of some graph operations

Authors

  • Abel Cabrera Martínez Universitat Rovira i Virgili, Departament d’Enginyeria Inform`atica i Matem`atiques, Spain
  • Suitberto Cabrera García Universitat Polit´ecnica de Valencia, Departamento de Estad´ıstica e Investigaci´on Operativa Aplicadas y Calidad, Spain
  • Iztok Peterin University of Maribor, Faculty of Electrical Engineering and Computer Science, Slovenia, and Inˇstitut za Matematiko, Fiziko in Mehaniko, Ljubljana, Slovenia
  • Ismael G. Yero Universidad de C´adiz, Departamento de Matem´aticas, Escuela T´ecnica Superior de Ingenier´ıa de Algeciras, Spain

DOI:

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

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.

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Published

2022-05-17

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