• Anil Kumar M S

Graph pebbling is a mathematical game played over a fixed graph. A pebbling distribution D is a function that assigns a number of pebbles to each vertex in a graph. A pebbling move removes two pebbles from one vertex and places a single pebble on an adjacent vertex. Thus, one pebble is lost with every move. A pebbling sequence is a list of pebbling moves performed in order under a distribution. A vertex is reachable under a distribution if it is possible to place a pebble on that vertex after some pebbling sequence.A vertex is reachable under a distribution if it is possible to place a pebble on that vertex after some pebbling sequence.A pebbling distribution is solvable if any chosen target vertex is reachable. In 2007, Christain Belford introduced an extension of graph pebbling called rubbling, Rubbling is similar to graph pebbling, but it allows for an additional type of move. A rubbling move is either a pebbling move or a strict rubbling move. A strict rubbling move onto a vertex v removes one pebble each from two of v's neighbors and places a single pebble on v. The rubbling number of a graph G, denoted ρ(G), as the smallest k ∈ N such that every initial distribution of k pebbles to G results in any vertex of G being reachable using rubbling moves. The rubbling number of tree,star,diameter two graphs are proved in this paper.

Pebbling,rubbling,diameter two graphs

"GRAPH RUBBLING PROBLEMS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 3, page no.40-42, March-2019, Available :http://www.jetir.org/papers/JETIR1903H49.pdf

"GRAPH RUBBLING PROBLEMS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 3, page no. pp40-42, March-2019, Available at : http://www.jetir.org/papers/JETIR1903H49.pdf