On Strongly Regular Graphs with m2 = qm3 AND m3 = qm2 FOR q = 7 2; 7 3; 7 4; 7 5; 7 6

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 and such
that jSi \ Sj j = for any two adjacent vertices i and j, and jSi \ Sj j = for any two distinct non-adjacent vertices i and j, where Sk denotes the neighborhood of the vertex
k. Let 1 = r, 2 and 3 be the distinct eigenvalues of a connected strongly regular graph. Let m1 = 1, m2 and m3 denote the multiplicity of r, 2 and 3, respectively. We
here describe the parameters n, r, and for strongly regular graphs with m2 = qm3 and m3 = qm2 for q = 7/2 ; 7/3 ; 7/4 ; 7/5 ; 7/6 .