Relatively prime restrained geodetic number of graphs

Abstract

In this paper we introduce relatively prime restrained geodetic set of graphs G. A set $S \subseteq V(G)$ is said to be relatively prime restrained geodetic set in $G$ if $S$ is a relatively prime geodetic set and $\langle V(G)-S\rangle$ has no isolated vertices. The relatively prime restrained geodetic set is denoted by $g_{r p r}(G)$ - set. The minimum cardinality of relatively prime restrained geodetic set is the relatively prime restrained geodetic number and it is denoted by $g_{r p r}(G)$.