DETOUR EDGE PEBBLING NUMBER IN GRAPHS
By
S. Vincylin1 and I. Gnanaselvi2
1,2Department of Mathematics, Sarah Tucker College, Tirunelveli, Tamilnadu, India - 627007.
Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli, Tamilnadu, India - 627012.
Email: 1Corresponding author: vincylin7@gmail.com, 2selvikim@gmail.com
(Received: January 07, 2024; In format: February 16, 2024; Revised: April 25, 2024; Accepted: July 09, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55201
Abstract
Assume G is a connected graph with distributing pebbles over its edges. An edge pebbling move on a graph G is defined to be the removal of two pebbles from one edge and one pebble will be added to an adjacent edge, while the other pebble will be discarded from the play. In this paper, we introduce the concept of detour edge pebbling number and find out the detour edge pebbling number for some standard graphs. We carry out the edge pebbling move in the concept of detour pebbling to arrive a new graph invariant called the detour edge pebbling number. The detour edge pebbling number of an edge e of a graph G is the minimum number of pebbles such that these pebbles are placed on the edges of G, we can move a pebble to e by making a sequence of pebble moves regardless of the initial configuration using the edge detour path. The detour edge pebbling number of a graph G, f* e(G), is the maximum f* e(G, e) over all the edges of G.
2020 Mathematical Sciences Classification: 05C12, 05C57, 05C38.
Keywords and Phrases: Edge pebbling move, Edge detour path, Edge detour distance, Detour edge pebbling number.