Restrained geodetic domination of edge subdivision graph

Abstract

For a connected graph [Formula: see text], a set [Formula: see text] subset of [Formula: see text] is said to be a geodetic set if all vertices in G should lie in some [Formula: see text] geodesic for some [Formula: see text]. The minimum cardinality of the geodetic set is the geodetic number. In this paper, the authors discussed the geodetic number, geodetic domination number, and the restrained geodetic domination of the edge subdivision graph.