Journal of Prime Research in Mathematics

# 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,

### 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.