Liwat, John Mark R. and Eballe, Rolito G.
(2023)
*Pointwise Clique-Safe Domination in Graphs.*
Asian Research Journal of Mathematics, 19 (9).
pp. 254-272.
ISSN 2456-477X

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## Abstract

Let G = (V (G),E (G)) be any finite, undirected, simple graph. The clique centrality of a vertex V (G), denoted by

G (), is the maximum size of a clique in G containing

. A set D V (G) is introduced in this paper as a pointwise clique-safe dominating set of G if for every vertex Dc there exists a vertex D such that E (G) where D G () Dc G (). The smallest cardinality of such a pointwise clique-safe dominating set of G is called the pointwise clique-safe domination number of G, denoted by pcs (G). This study aims to generate some observable properties of the parameter and to evaluate the minimum pointwise clique-safe dominating sets of some special families of graphs such as the complete graph K, fan graph F, wheel graph W and complete bipartite K

,as well as graphs obtained under the mycielski operation.

Item Type: | Article |
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Subjects: | Eprint Open STM Press > Mathematical Science |

Depositing User: | Unnamed user with email admin@eprint.openstmpress.com |

Date Deposited: | 19 Sep 2023 11:20 |

Last Modified: | 19 Sep 2023 11:20 |

URI: | http://library.go4manusub.com/id/eprint/1052 |