The t-pebbling number of Jahangir graph J3,m
DOI:
https://doi.org/10.4067/S0716-09172015000200005Keywords:
Pebbling number, Jahangir graph.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.References
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[6] A. Lourdusamy, S. Samuel Jayaseelan and T. Mathivanan, Pebbling number for Jahangir graph J2,m (3 < m < 7), Sciencia Acta Xaveriana Vol. 3 (1), pp. 87-106, (2012).
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[9] A. Lourdusamy and S. Somasundaram, The t-pebbling number of graphs, South East Asian Bulletin of Mathematics, 30, pp. 907-914, (2006).
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[12] L. Pachter, H.S. Snevily and B. Voxman, On pebbling graphs, Congressus Numerantium, 107, pp. 65-80, (1995).
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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).
[3] A. Lourdusamy, and T. Mathivanan, The pebbling number of the Jahangir graph J2,m, Submitted for publication.
[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).
[5] A. Lourdusamy and A. Punitha Tharani, On t-pebbling graphs, Utilitas Mathematica (To appear in Vol. 87, March 2012).
[6] A. Lourdusamy, S. Samuel Jayaseelan and T. Mathivanan, Pebbling number for Jahangir graph J2,m (3 < m < 7), Sciencia Acta Xaveriana Vol. 3 (1), pp. 87-106, (2012).
[7] A. Lourdusamy, S. Samuel Jayaseelan and T. Mathivanan, On pebbling Jahangir graph, General Mathematics Notes, 5 (2), pp. 42-49, (2011).
[8] A. Lourdusamy, S. Samuel Jayaseelan and T. Mathivanan, The tpebbling number of Jahangir graph, International Journal of Mathematical Combinatorics, Vol. 1, pp. 92-95, (2012).
[9] A. Lourdusamy and S. Somasundaram, The t-pebbling number of graphs, South East Asian Bulletin of Mathematics, 30, pp. 907-914, (2006).
[10] D. Moews, Pebbling graphs, J. Combin, Theory Series B, 55, pp. 244- 252, (1992).
[11] D. A. Mojdeh and A. N. Ghameshlou, Domination in Jahangir graph J2,m, Int. J. Contemp. Math. Sciences, 2, No. 24, pp. 1193-1199, (2007).
[12] L. Pachter, H.S. Snevily and B. Voxman, On pebbling graphs, Congressus Numerantium, 107, pp. 65-80, (1995).
[13] C. Xavier and A. Lourdusamy, Pebbling numbers in graphs, Pure Appl. Math. Sci., 43, No. 1-2, pp. 73-79, (1996).
How to Cite
[1]
A. Lourdusamy and T. Mathivanan, “The t-pebbling number of Jahangir graph J3,m”, Proyecciones (Antofagasta, On line), vol. 34, no. 2, pp. 161-174, 1.
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