Total Domination on Some Graph Operators

José M. Sigarreta
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José M. Sigarreta: Faculty of Mathematics, Autonomous University of Guerrero, Carlos E. Adame 5, Col. La Garita, C. P. 39350 Acapulco, Mexico

Mathematics, 2021, vol. 9, issue 3, 1-9

Abstract: Let G = ( V , E ) be a graph; a set D ⊆ V is a total dominating set if every vertex v ∈ V has, at least, one neighbor in D . The total domination number γ t ( G ) is the minimum cardinality among all total dominating sets. Given an arbitrary graph G , we consider some operators on this graph; S ( G ) , R ( G ) , and Q ( G ) , and we give bounds or the exact value of the total domination number of these new graphs using some parameters in the original graph G .

Keywords: domination theory; total domination; graph operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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