On the distance pattern distinguishing number of a graph

Let g = (v,e) be a connected simple graph and let m be a nonempty subset of v. the m -distance pattern of a vertex u in g is the set of all distances from u to the vertices in m. if the distance patterns of all vertices in v are distinct,then the set m is a distance pattern distinguishing set of g. a graph g with a distance pattern distinguishing set is called a distance pattern distinguishing graph. minimum number of vertices in a distance pattern distinguishing set is called distance pattern distinguishing number of a graph. this paper initiates a study on the problem of finding distance pattern distinguishing number of a graph and gives bounds for distance pattern distinguishing number. further,this paper provides an algorithm to determine whether a graph is a distance pattern distinguishing graph or not and hence to determine the distance pattern distinguishing number of that graph. © 2014 sona jose and germina k. augustine.