Journal of Prime Research in Mathematics

# 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

### 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.