Relatively prime geodetic number of graphs

Abstract

In this paper we introduce relatively prime geodetic number of a graph \(G\). Let \(G\) be a connected graph. A set \(S \subseteq V\) is said to be a relatively prime geodetic set if it is a geodetic set with at least three elements and the shortest distance between any two pairs of vertices in \(S\) is relatively prime. The relatively prime geodetic set of \(G\) is denoted by \(g_{r p}(G)\)-set. The cardinality of a minimum relatively prime geodetic set is the relatively prime geodetic number and it is denoted \(g_{r p}(G)\).