Domination, Total Domination and Open Packing of the Corcor Domain of Graphene

Abstract

A dominating set of a graph G = (V,E) is a subset D of V such that everyvertex not in D is adjacent to at least one vertex in D. A dominating set D is a totaldominating set, if every vertex in V is adjacent to at least one vertex in D. The set Pis said to be an open packing set if no two vertices of P have a common neighbor inG. In this paper, we obtain domination number, total domination number and openpacking number of the molecular graph of a new type of graphene named CorCor thatis a 2-dimensional carbon network.