Clique doubly connected domination in the join and lexicographic product of graphs

Enrico L. Enriquez; Albert D. Ngujo

doi:10.1142/S1793830920500664

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Clique doubly connected domination in the join and lexicographic product of graphs

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Enrico L. Enriquez, Albert D. Ngujo

2020 Discrete Mathematics, Algorithms and Applications Vol. 12 Issue 5 Article Cited by 1

Abstract

Let G be a connected simple graph. A set S ⊆ V (G) is a doubly connected dominating set if it is dominating and both 〈S〉 and 〈V (G)\S〉 are connected. A nonempty subset S of the vertex set V (G) is a clique in G if the graph 〈S〉 induced by S is complete. A clique dominating set S of G is a clique doubly connected dominating set if S is a doubly connected dominating set of G. The clique doubly connected domination number of G, denoted by γcld(G), is the smallest cardinality of a clique doubly connected dominating set S of G. In this paper, we give the characterization of the clique doubly connected dominating set and the clique doubly connected domination number in the join (and lexicographic product) of two graphs. © 2020 World Scientific Publishing Co. Pte Ltd. All rights reserved.

Affiliations

Department of Computer, Information Sciences and Mathematics, School of Arts and Sciences, University of San Carlos, Cebu City, 6000, Philippines

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