Detour Pebbling Number on Some Commutative Ring Graphs

Abstract

. The detour pebbling number of a graph G is the least positive integer f ∗ ( G ) such that these pebbles are placed on the vertices of G , we can move a pebble to a target vertex by a sequence of pebbling moves each move taking two pebbles off a vertex and placing one of the pebbles on an adjacent vertex using detour path. In this paper, we compute the detour pebbling number for the commutative ring of zero-divisor graphs, sum and the product of zero divisor graphs.