The t-pebbling number of some wheel related graphs

A. Lourdusamy
Department of Mathematics, St. Xavier’s College (Autonomous), Palayamkottai – 627 002, Tamilnadu, India.
F. Patrick
Department of Mathematics, St. Xavier’s College (Autonomous), Palayamkottai – 627 002, Tamilnadu, India.
T. Mathivanan
Department of Mathematics, St. Xavier’s College (Autonomous), Palayamkottai – 627 002, Tamilnadu, India.

\(^{1}\)Corresponding Author: lourdusamy15@gmail.com

Copyright © 2016 A. Lourdusamy, F. Patrick, T. Mathivanan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2016.

Abstract

Let \(G\) be a graph and some pebbles are distributed on its vertices. A pebbling move (step) consists of removing two pebbles from one vertex, throwing one pebble away, and moving the other pebble to an adjacent vertex. The t-pebbling number of a graph \(G\) is the least integer \(m\) such that from any distribution of m pebbles on the vertices of \(G\), we can move t pebbles to any specified vertex by a sequence of pebbling moves. In this paper, we determine the t-pebbling number of some wheel related graphs.

Keywords:

Pebbling number, Wheel graphs.