The Connected Geodetic Global Domination Number of a Graph

Abstract

A set S of vertices in a connected graph {G=(V,E)} is called a geodetic set if every vertex not in S lies on a shortest path between two vertices from S. A set D of vertices in G is called a dominating set of G if every vertex not in D has at least one neighbour in D. A geodetic dominating set S is both a geodetic and a dominating set. A set S is called a
geodetic global dominating set of G if S is both geodetic and global dominating set of G. The geodetic global domination number (geodetic domination number) is the minimum
cardinality of a geodetic global dominating set (geodetic dominating set) in G. In this paper we introduced and investigate the connected geodetic global domination number of certain graphs and some of the general properties are studied.