The domination cover pebbling number of the square of a path

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

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

Copyright © 2011 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, 2011.

Abstract

Given a configuration of pebbles on the vertices of a connected graph \(G\), a pebbling move (or pebbling step) is defined as the removal of two pebbles from a vertex and placing one pebble on an adjacent vertex. The domination cover pebbling number, \(ψ(G)\), of a graph \(G\) is the minimum number of pebbles that have to be placed on \(V (G)\) such that after a sequence of pebbling moves, the set of vertices with pebbles forms a dominating set of \(G\), regardless of the initial configuration. In this paper, we determine the domination cover pebbling number for the square of a path.

Keywords:

Pebbling, square of a path, cover pebbling, domination.