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 .

A sum divisor cordial labeling of a graph G with vertex set V is a bijection f from V (G) to {1, 2, · · · , |V (G)|} such that an edge uv is assigned the label 1 if 2 divides f (u) + f (v) and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a sum divisor cordial labeling is called a sum divisor cordial graph. In this paper, we prove that path, comb, star, complete bipartite, K 2 + mK 1 , bistar, jewel, crown, flower, gear, subdivision of the star, K 1,3 * K 1,n and square graph of B n,n are sum divisor cordial graphs.Subjclass : 05C78.

We introduce a new type of labeling known as vertex equitable labeling. We study the Properties of this labeling and we investigate vertex equitable behaviors of some standard graphs. We also prove that arbitrary supersubdivision of paths is vertex equitable and that every cycle C n with n ≡ 0 or 3 (mod 4) has a vertex equitable superdivision.

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Let G be a connected graph. A pebbling move is defined as taking two pebbles from one vertex and placing one pebble to an adjacent vertex and throwing away the other pebble. The non-split domination cover pebbling number, ψ ns (G), of a graph G is the minimum of pebbles that must be placed on V (G) such that after a sequence of pebbling moves, the set of vertices with a pebble forms a non-split dominating set of G, regardless of the initial configuration of pebbles. We discuss some basic results, NP-completeness of non-split domination number, and determine ψ ns for some families of Middle graphs.