Pebbling In Watkins Snark Graph
Ms.Sreedevi S, Dr.M.S Anilkumar - · International Journal of Research in Advent Technology · 2019
The pebbling theory is a study of a mathematical game that is played over a graph.In this game, a pebbling movement means removing two pebbles from a given vertex and adding one pebble to one of its neighbors and removing the other pebble from the game.The pebbling number of a graph G is defined a smallest positive integer required to add a pebble at any target vertex of the graph.It is denoted as .Every vertex of the graph is pebbled irrespective of the initial pattern of pebbles.Cubic graph is also called a 3-regular graph which is used in a real time scenario.In this paper, we have determined the pebbling number of Watkins Snark by constructing a Watkins Flower Snark of vertices, edges, cycles and disjoint sets which are present in the Watkins Snark.It is a connected graph in which bridgeless cubic index is equal to 4 with 75 edges and 50 vertices.