• (r, 2, (r – 2) (r – 1))- REGULAR GRAPHS

Abstract

A graph G is said to be (r, 2, k) - regular graph if d (v) = r and d 2 (v) = k, for all v in G, where d 2 (v) be the number of vertices that are at distance 2 from v in a given graph G. A graph G is called ( r, 2, ( r - 2) ( r -1 ))- regular if each vertex in the graph G is at a distance one from exactly r number of vertices and at a distance two from exactly (r-2) (r-1) number of vertices.That is d(v) = r and d2(v) = (r-2) (r-1), for all v in G. In this paper, we suggest a method to construct for any r ≥ 2, (r, 2, (r-2) (r-1)) - regular graph on 3 x 2r-2 vertices.