GEODETIC HUB NUMBER OF GRAPHS

Abstract

A subset $S$ of vertex set $V(G)$ of a graph $G$ of order $n\geq 2$ is a geodetic hub set of $G$ if $S$ is both a geodetic set and a hub set of $G$. The minimum cardinality of a geodetic hub set of $G$ is called the geodetic hub number of $G$, denoted by $h_{geo}(G)$. In this paper, we initiate the study of geodetic hub number of a graph. The geodetic hub number of several classes of graphs are determined and its value for some graph operations are studied.