Pebbling on zig-zag chain graph of n odd cycles

A Lourdusamy,J Jenifer Steffi

doi:10.22199/issn.0717-6279-2019-03-0038

Abstract

Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move on G consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The pebbling number of G, f (G), is the least n such that any distribution of n pebbles on G allows one pebble to be reached to any specified, but an arbitrary vertex. Similarly, the t−pebbling number of G, ft(G), is the least m such that from any distribution of m pebbles, we can move t pebbles to any specified, but an arbitrary vertex. In this paper, we determine the pebbling number, and the t−pebbling number of the zigzag chain graph of n copies of odd cycles.

Highlights

In this work it is considered undirected simple graphs that are connected
Pebbling in graph was first suggested by Lagarias and Saks and it was introduced in the literature by Chung [2]
[14] In a zig-zag chain graph of n copies of even cycles C2k, denoted by ZZn(C2k) with a specified vertex v, the following are true for k ≥ 3

Summary

Introduction

In this work it is considered undirected simple graphs that are connected. For some other graph theoretical concepts the reader should refer to [1]. With regard to pebbling number and t−pebbling number of various classes of graphs, we invite the readers to refer to [2, 4, 9, 10], and [11] Motivated by these works, we compute the pebbling number and the t−pebbling number of zig-zag chain graph of n copies of odd cycles. [14] In a zig-zag chain graph of n copies of even cycles C2k, denoted by ZZn(C2k) with a specified vertex v, the following are true for k ≥ 3. Let ZZ2(C2k+1) be the zig-zag chain graph of two copies of odd cycles

Consider the graph

Then by