The 2t−Pebbling Property on the Zig-Zag Chain Graph of n Odd Cycles A. Lourdusamy 1 and J. Jenifer Steffi 2 1,2 St. Xavier’s College (Autonomous), Palayamkottai- 627002, Tamilnadu, India. 1 lourdusamy15@gmail.com 2 jenifersteffi.j@gmail.com Abstract A graph G has the 2t−pebbling property if for any distribution with more than 2f t (G) − q pebbles, it is possible, using the sequence of pebbling moves, to put 2t pebbles on any vertex. In this paper, we show that the zig-zag chain graph of n copies of odd cycles satisfies the two-pebbling property and the 2t−pebbling property. AMS Subject Classification: 05C 99 Key Words and Phrases: Graph pebbling, zig-zag chain graph. 1 Introduction Throughout this paper, when we speak of a graph G, we consider only simple and connected graphs. For the definition of other graph theoritical terms, we refer to [1]. Frequently, the letter v will be used to denote the specified vertex of the graph under consideration. Let D be a distribution of pebbles on the vertices of G. Let p(v) denote the number of pebbles distributed on the vertex v and let p(G)= ∑ v∈V (G) p(v). The operation of pebbling movement is called a pebbling step, defined as removing two pebbles from a vertex and adding one on an adjacent vertex. To understand the pebbling concepts, we need the following definitions. Definition 1. [2] [3] The pebbling number of G, f (G), and the t-pebbling number of G, f t (G), are the smallest numbers, such that from any placement of f (G) pebbles or f t (G) pebbles, it is possible to move one or t pebbles, respectively, to any specified vertex by a sequence of pebbling moves. Thus, f (G) and f t (G) are the maximum values of f (G, v) and f t (G, v) over all vertices v. International Journal of Pure and Applied Mathematics Volume 117 No. 14 2017, 209-218 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu Special Issue ijpam.eu 209