Some Induced Subgraphs of Strongly Regular Graphs with no Triangles

Let G be a strongly regular graph with no triangles (SRNT graph) with the parameters (n, k, 0, µ) , if v is a vertex of G, a subgraph which induced by the set of vertices at distance one denoted by G1(v) and subgraph which induced by the set of vertices at distance two denoted by G2(v). In this paper we introduce and study the subgraph which induced by the set U and denoted by G2(U) where, U can be defined as U = {x: x ∈ V (G), d(a, x) = d(b, x) = 2, and a, b are adjacent vertices}