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 $g_{r p}(G)$.