2-pebbling property of butterfly-derived graphs. (15th December 2021)

• Record Type: Journal Article
• Authors: Punitha, M. Joice; Suganya, A. Sagaya
• Is Part Of: International journal of dynamical systems and differential equations. Volume 11:Number 5/6(2021)
• Page Start: 566
• Page End: 578
• Publication Date: 2021-12-15
• Subjects: pebbling -- 2-pebbling -- butterfly graph -- Benes graph -- augmented butterfly graph -- enhanced butterfly graph; Differential equations -- Periodicals; 515.35
• Languages: English
• ISSNs: 1752-3583

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.