On the neighbor-distinguishing in generalized Petersen graphs

Abstract

In a connected graph G, two adjacent vertices are said to be neighbors of each other. A vertex v adjacently distinguishes a pair (x,y) of two neighbors in G if the number of edges in v-x geodesic and the number of edges in v-y geodesic differ by one. A set S of vertices of G is a neighbor-distinguishing set for G if every two neighbors in G are adjacently distinguished by some element of S. In this paper, we consider two families of generalized Petersen graphs and distinguish every two neighbors in these graphs by investigating their minimum neighbor-distinguishing sets, which are of coordinately two.

Keywords

• distinguishing set
• neighbor-distinguishing set
• generalized petersen graphs