On the Distance Pattern Distinguishing Number of a Graph

الملخص EN

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.