THE ECCENTRIC HUB NUMBER OF A GRAPH

Abstract

A set $H \subseteq V(G)$ is eccentric hub set of a graph $G$ if $H$ is a hub set of $G$ and also every $v \in V(G) \backslash H$ has an eccentric vertex in $H$. The minimal eccentric hub set with minimum cardinality is called minimum eccentric hub set. Its cardinality is eccentric hub number of $G$, denoted by $e h(G)$. In this paper, we deduce some results and bounds on this parameter. Further, we have studied about total number of minimum eccentric hub sets and eccentric hub graphs. Received: June 14, 2023; Accepted: August 2, 2023