Abstract

Cover Pebbling Number of Some Cycle Related Graphs

Joice Punitha M1 and Sagaya Suganya A

1Department of Mathematics,
Bharathi Women's College, Chennai, India
Department of Mathematics and Actuarial Science,
B. S. Abdur Rahman Crescent Institute of Science & Technology, Chennai, INDIA

ABSTRACT

Given a configuration of pebbles on the vertices of a connected graph G, a pebbling move is defined as the removal of two pebbles from a vertex and placing one pebble on an adjacent vertex. A configuration on a graph G is cover solvable if with an initial configuration of pebbles placed on the vertices of G, it is possible to place one pebble on every vertex of the graph through a sequence of pebbling move. The cover pebbling number of a graph γ (G) is defined as the smallest number such that every configuration of this size is cover solvable. In this paper, we have determined the results for γ (G) for Hex graph, Hex derived graphs and mth power of cycle.

Keywords :2010 AMS Subject Classification: 05C12, 05C57, 05C70.

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