The total co-independent domination number of some graph operations

  1. Abel Cabrera Martínez 1
  2. Suitberto Cabrera García 2
  3. Iztok Peterin 3
  4. Ismael G. Yero 4
  1. 1 Universitat Rovira i Virgili, Spain
  2. 2 Universitat Politècnica de València, Spain
  3. 3 University of Maribor, Slovenia
  4. 4 Universidad de Cádiz, Spain
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Journal:
Revista de la Unión Matemática Argentina

ISSN: 1669-9637,  0041-6932

Year of publication: 2022

Volume: 63

Issue: 1

Pages: 153-168

Type: Article

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More publications in: Revista de la Unión Matemática Argentina

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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