The t-pebbling number of Jahangir graph J₃,_m

A. Lourdusamy

T. Mathivanan

St. Xavier’s College (Autonomous)

India 

---

ABSTRACT

The t-pebbling number, f_t(G), of a connected graph G, is the smallest positive integer such that from every placement of f_t(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 J_3,m and finally we give a conjecture for the t-pebbling number of the graph J_n,m.

2010 Mathematics Subject Classification : 05C99.

Keywords : Pebbling number, Jahangir graph.

---

REFERENCES

[1] F.R.K. Chung, Pebbling in hypercubes, SIAM J. Disc. Math., 2 (4), pp. 467-472, (1989).

[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 J^,_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 t-pebbling 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. 244252, (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, Congres-sus 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).

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