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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.34 no.2 Antofagasta jun. 2015

http://dx.doi.org/10.4067/S0716-09172015000200005 

The t-pebbling number of Jahangir graph J3,m

A. Lourdusamy

T. Mathivanan

St. Xavier’s College (Autonomous)

India 


ABSTRACT

The t-pebbling number, ft(G), of a connected graph G, is the smallest positive integer such that from every placement of ft(G) pebbles, t pebbles can be moved to any specified target vertex by a sequence of pebbling moves, each move removes two pebbles of a vertex and placing one on an adjacent vertex. In this paper, we determine the t-pebbling number for Jahangir graph J3,m and finally we give a conjecture for the t-pebbling number of the graph Jn,m.

2010 Mathematics Subject Classification : 05C99.

Keywords : Pebbling number, Jahangir graph.


REFERENCES

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[2]    A. Lourdusamy, t-pebbling the graphs of diameter two, Acta Ciencia Indica, XXLX (M. No.3), pp. 465-470, (2003).         [ Links ]

[3]    A. Lourdusamy, and T. Mathivanan, The pebbling number of the Jahangir graph J2,m, Submitted for publication.         [ Links ]

[4]    A. Lourdusamy, C. Muthulakshmi @ Sasikala and T. Mathivanan, The pebbling number of the square of an odd cycle, Sciencia Acta Xaveriana Vol. 3 (2), pp. 21-38, (2012).         [ Links ]

[5]    A. Lourdusamy and A. Punitha Tharani, On t-pebbling graphs, Utilitas Mathematica (To appear in Vol. 87, March 2012).         [ Links ]

[6]    A. Lourdusamy, S. Samuel Jayaseelan and T. Mathivanan, Pebbling number for Jahangir graph J^,m (3 < m < 7), Sciencia Acta Xaveriana Vol. 3 (1), pp. 87-106, (2012).         [ Links ]

[7]    A. Lourdusamy, S. Samuel Jayaseelan and T. Mathivanan, On pebbling Jahangir graph, General Mathematics Notes, 5 (2), pp. 42-49, (2011).         [ Links ]

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[13]    C. Xavier and A. Lourdusamy, Pebbling numbers in graphs, Pure Appl. Math. Sci., 43, No. 1-2, pp. 73-79, (1996).         [ Links ]

A. Lourdusamy

Department of Mathematics St. Xavier’s College (Autonomous), Palayamkottai - 627 002, Tamilnadu,

India

e-mail : lourdusamy15@gmail.comT. Mathivanan

Department of Mathematics St. Xavier’s College (Autonomous), Palayamkottai - 627 002, Tamilnadu,

India

e-mail : tahiCvamman@yahoo.com

Received : December 2014. Accepted : April 2015

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