CLIQUE DOUBLY CONNECTED DOMINATION IN THE CORONA AND CARTESIAN PRODUCT OF GRAPHS

Enrico Limbo Enriquez, Grace M. Estrada, Valerie Verallo Fernandez, Carmelita M. Loquias, Albert D. Ngujo

Abstract


Let be a connected simple graph. A set  is a doubly connected dominating set if it is dominating and both and are connected. The doubly connected domination number of denoted by  is the smallest cardinality of a doubly connected dominating set ofA nonempty subsetof the vertex setis a clique in if the graph induced byis complete. A cliquein is a clique dominating set if it is a dominating set. A clique dominating set ofis a clique doubly connected dominating set if is a doubly connected dominating set of The clique doubly connected domination number of, denoted by  is the smallest cardinality of a clique doubly connected dominating set  of In this paper, we show that every integersand with  is realizable as clique doubly connected domination number and order of  respectively. Further, we give the characterization of the clique doubly connected dominating set with a clique doubly connected domination numbers of 1 and 2. Finally, we characterize the clique doubly connected dominating sets of the corona and Cartesian product of two graphs.

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