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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.3 Antofagasta ago. 2019

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

Articles

Pebbling on zig-zag chain graph of n odd cycles

A. Lourdusamy1 
http://orcid.org/0000-0001-5961-358X

J. Jenifer Steffi2 

1St. Xavier’s College (Autonomous), Department of Mathematics, Palayamkottai - 627 002, Tamil Nadu, India. e-mail: lourdusamy15@gmail.com

2 Manonmaniam Sundaranar University, PHD Student, Abisekapatti, Tamil Nadu, India. e-mail: jenifersteffi.j@gmail.com

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.

Keywords: Graph pebbling; Zig-zag chain graph

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

References

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Received: May 2018; Accepted: July 2018

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