Pebbling on Jahangir graphs

TL;DR

This paper determines the pebbling number of Jahangir graphs $J_{n,m}$ with even $n$ and $m \,geq\,8$, expanding understanding of pebbling properties in specific graph families.

Contribution

It provides the first explicit calculation of the pebbling number for Jahangir graphs with even $n$ and $m\geq8$, a previously unstudied class.

Findings

Pebbling number of $J_{n,m}$ with even $n$ and $m\geq8$ is established.

Methodology for calculating pebbling numbers in Jahangir graphs is developed.

Results contribute to graph pebbling theory and its applications.

Abstract

The pebbling number of a graph $G$, $f(G)$, is the least $p$ such that, however $p$ pebbles are placed on the vertices of $G$, we can move a pebble to any vertex by a sequence of moves, each move taking two pebbles off one vertex and placing one on an adjacent vertex. In this paper, we will show the pebbling number of Jahangir graphs $J_{n,m}$ with $n$ even, $m\geq8$.