Strong doubly edge geodetic problem in graphs

Abstract

For a graph G(V(G), E(G), the problem to find a set S ⊆ V(G) where every edge in E(G) is covered by least two fixed geodesics between the vertices in S is called the strong doubly edge geodetic problem and the cardinality of the smallest such S is the strong doubly edge geodetic number of G. In this paper the computational complexity for strong doubly edge geodetic problem is studied and also some bounds for general graphs are derived.