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.

Keywords and Phrases

Hub set, Hub number, Geodetic set, Geodetic number.

A.M.S. subject classification

05C07, 05C69, 05C90.

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