Geodetic parameters in tree derived architectures

Abstract

A geodetic cover of a graph G refers to a subset of vertices of G that covers all the vertices of G using the shortest paths between the vertices in the set and the cardinality of a minimum geodetic cover is the geodetic number of the graph G, denoted by g(G). This paper is devoted to the study of the geodetic number, the strong geodetic number, the edge geodetic number and the strong edge geodetic number of certain tree derived architectures.