• ON THE SUBSET GRAPH OF A NEAR-RING

Abstract

Let N be a near-ring.  Let F be the collection of all non-empty subsets of N. We define a new graph, the  subset  graph     as the  graph  with  all the  members of F as  vertices  and  any  two  distinct vertices A, B  are  adjacent  if and  only  if A+B = {a + b: a∈A, b∈B}is a right N - subset  of N. In this paper we discuss about the connectivity, diameter and girth of the graph FR. We also discuss about some induced subgraphs of FR and some graphical parameters of these subgraphs viz .diameter, girth etc.