Title: 2-pebbling property of butterfly-derived graphs

Authors: M. Joice Punitha; A. Sagaya Suganya

Addresses: Department of Mathematics, Bharathi Women's College, Chennai, 600108, India ' Department of Mathematics and Actuarial Science, B. S. Abdur Rahman Crescent Institute of Science and Technology, Chennai, 600048, India

Abstract: For a graph G, f(G) is the least distribution of p pebbles on the vertices of G, so that we can move a pebble to any vertex by a sequence of moves and each move is taking two pebbles off one vertex and placing one pebble on an adjacent vertex. A graph G is said to satisfy 2-pebbling property, if it is possible to move two pebbles to any arbitrarily chosen vertex with a possible distribution of 2f(G) - q + 1 pebbles, where q is the number of vertices with at least one pebble. This paper determines the pebbling number and the 2-pebbling property of butterfly derived graphs.

Keywords: pebbling; 2-pebbling; butterfly graph; Benes graph; augmented butterfly graph; enhanced butterfly graph.

DOI: 10.1504/IJDSDE.2021.120050

International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.5/6, pp.566 - 578

Accepted: 10 Jul 2020
Published online: 05 Jan 2022 *

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