Algorithmic Aspects of k-Geodetic Sets in Graphs

Abstract

Let G be a connected graph of order $p\ge 2$. We study about the geodetic sets and k-geodetic sets of G. We study link vectors and prove a theorem to develop an algorithm to find the k-geodetic sets. Initially we study algorithms to find the closed interval between any two vertices of G and to find it's link vectors. In this paper we present two algorithms to check whether a given set of vertices is a k-geodetic set and to find the minimum k-geodetic set of G.