DETOUR PEBBLING ON CARTESIAN PRODUCT GRAPHS

Lourdusamy .; S. Saratha Nellainayaki

doi:10.56827/SEAJMMS.2022.1803.30

Lourdusamy . Department of Mathematics, St. Xavier’s College (Autonomous), Palayamkottai - 627002, Tamil Nadu, INDIA
S. Saratha Nellainayaki Department of Mathematics, Vyasa Arts and Science Women’s College, Subramaniapuram, Tamilnadu, INDIA

DOI: https://doi.org/10.56827/SEAJMMS.2022.1803.30

Abstract

Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move is defined as the removal of two pebbles from some vertex and the placement of one of those pebbles on an adjacent vertex. The t - pebbling number of G is the smallest number, f_t(G) such that from any distribution of f_t(G) pebbles, it is possible to move t pebbles to any specified target vertex by a sequence of pebbling moves. The detour pebbling number of a graph f ^∗(G) is the smallest number such that from any distribution of f ^∗(G) pebbles, it is possible to move a pebbles to any specified target vertex by a sequence of pebbling moves using a detour path. In this paper, we find the detour pebbling number for some Cartesian product graphs and also the detour t - pebbling number for those cartesian product graphs.