THE NUMBER OF CC-DOMINATING SETS OF SOME GRAPHS

Priya K; Anil Kumar V

doi:10.56827/SEAJMMS.2023.1902.15

Priya K Department of Mathematics, University of Calicut, Malappuram - 673635, Kerala, INDIA
Anil Kumar V Department of Mathematics, University of Calicut, Malappuram - 673635, Kerala, INDIA

DOI: https://doi.org/10.56827/SEAJMMS.2023.1902.15

Keywords: CC-Domination Polynomial, CC-Domination Number, Closely-connected Vertices, CC-Degree of a Vertex, CC-Isolated Vertex, CCDomination Entropy.

Abstract

The aim of this paper is to study about the number of cc-dominating sets and to introduce the concept of cc-domination polynomial for simple finite undirected graphs. For a graph G on n vertices possessing dc(G, i) cc-dominating sets of cardinality i, the cc-domination polynomial is defined as Dc[G; x] = Pn i=Γcc(G) dc(G, i)xi, where Γcc(G) is the cc-domination number of G. We obtain some properties of Dc[G; x] and compute the same for some special graphs. Moreover, the concept of cc-domination entropy is also introduced and studied