Path-Induced Closed Geodetic Domination of Some Common Graphs and Edge Corona of Graphs

Abstract

Let G be a connected graph of order n and S ⊆ V (G). A closed geodetic cover S of Gis a path-induced closed geodetic dominating set of a graph G if a subgraph <S> has a Hamiltonianpath and S is a dominating set of G. The minimum cardinality of a path-induced closed geodeticdominating set is called path-induced closed geodetic domination number of G. This study presentsthe characterization of the path-induced closed geodetic dominating sets of some common graphsand edge corona of two graphs. The path-induced closed geodetic domination numbers of thesegraphs are also determined.