The open  hub number of a graph

Ragi Puthan Veettil 1 * and T.V. Ramakrishnan 2

doi:10.26637/MJM0804/0006

The open hub number of a graph

Authors :

Ragi Puthan Veettil ^{1 *} and T.V. Ramakrishnan ²

Author Address :

¹ Department of Mathematics, PRNSS College, Mattanur-670702, Kerala, India.
² Department of Mathematics, Kannur University, Kannur-670002, Kerala, India.

*Corresponding author.

Abstract :

Let $G = (V, E)$ be a connected graph. A subset $H$ of $V$ is called a hub set of $G$ if for any two distinct vertices $u,v \in V-H,$ there exists a $u$-$v$ path $P$ in $G$ such that all the internal vertices of $P$ are in H .A hub set $H$ of $V$ is called an open hub set if the induced sub graph $<H>$ has no isolated vertices.The minimum cardinality of an open hub set of $G$ is called the open hub number of $G$ and is denoted by $h_O(G)$. In this paper, we present several basic results on the open hub number.

Keywords :

Open hub set, Open hub number.

DOI :

10.26637/MJM0804/0006

Article Info :

Received : April 29, 2020; Accepted : August 30, 2020.