On Strongly Regular Graphs with m<inf>2</inf>= qm<inf>3</inf>AND m<inf>3</inf>= qm<inf>2</inf>Where q ∈ ℚ

Abstract

We say that a regular graph G of order n and degree r ≥ 1 (which is not the complete graph) is strongly regular if there exist non-negative integers т and θ such that |Si∩ Sj| = λ for any two adjacent vertices i and j, and |Si∩ Sj| = θ for any two distinct non-adjacent vertices i and j, where Skdenotes the neighborhood of the vertex k. Let λ1= r, λ2and λ3 be the distinct eigenvalues of a connected strongly regular graph. Let m1= 1, m2and m3 denote the multiplicity of r, λ2and λ3, respectively. We here describe the parameters n, r, λ and θ for strongly regular graphs with m2= qm3and m3= qm2for q = (Formula preasented).