Enrico L. Enriquez, Albert D. Ngujo
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.
Department of Computer, Information Sciences and Mathematics, School of Arts and Sciences, University of San Carlos, Cebu City, 6000, Philippines
