(untitled) (European Journal of Pure and Applied Mathematics, 2023)
Let G be a connected graph of order n and S ⊆ V (G). A closed geodetic cover S of G is a path-induced closed geodetic dominating set of a graph G if a subgraph <S> has a Hamiltonian path and S is a dominating set of G. The minimum cardinality of a path-induced closed geodetic dominating set is called path-induced closed geodetic domination number of G. This study presents the characterization of the path-induced closed geodetic dominating sets of some common graphs and edge corona of two graphs. The path-induced closed geodetic domination numbers of these graphs are also determined.