Covering cover pebbling number for square of a cycle

A. Lourdusamy
Department of Mathematics, St. Xavier’s College (Autonomous), Palayamkottai, India.
T. Mathivanan
Department of Mathematics, St. Xavier’s College (Autonomous), Palayamkottai, India.

\(^{1}\)Corresponding Author: lourdugnanam@hotmail.com,

Copyright © 2012 A. Lourdusamy, 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, 2012.

Abstract

Let \(G\) be a connected graph. Let p be the number of pebbles distributed on the vertices of \(G\). A pebbling move is defined by removing two pebbles from one vertex and put a pebble on an adjacent vertex. The covering cover pebbling number, \(σ(G)\), is the least p such that after a sequence of pebbling moves, the set of vertices should form a covering for \(G\) from every configuration of p pebbles on the vertices of \(G\). In this paper, we determine the covering cover pebbling number for square of a cycle.

Keywords:

Graph pebbling, cover pebbling, covering, square of a cycle.