The \(t\)-pebbling number of squares of cycles

Lourdusamy Arockiam
Department of Mathematics, St. Xavier’s College (Autonomous), Palayamkottai – 627 002, Tamilnadu, India.
Mathivanan Thanaraj
Department of Mathematics, St. Xavier’s College (Autonomous), Palayamkottai – 627 002, Tamilnadu, India.

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

Copyright © 2015 Lourdusamy Arockiam, Mathivanan Thanaraj. 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, 2015.

Abstract

Let \(C\) be a configuration of pebbles on a graph \(G\). 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, \(f_t(G)\), of a connected graph \(G\), is the smallest positive integer such that from every configuration of \(f_t(G)\) pebbles, t pebbles can be moved to any specified target vertex by a sequence of pebbling moves. In this paper, we determine the t-pebbling number for squares of cycles.

Keywords:

Pebbling number, \(p^{th}\) power of a graph, cycle graph.