A Survey on Strongly Regular Graphs with $m_2 = qm_3$' and $m_3 = qm_2$
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Authors: M. LEPOVIć
DOI: 10.46793/KgJMat2609.1513L
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 τ and ???? such that |Si ∩Sj| = τ for any two adjacent vertices i and j, and |Si ∩Sj| = ???? for any two distinct non-adjacent vertices i and j, where Sk denotes the neighborhood of the vertex k. Let λ1 = r, λ2 and λ3 be the distinct eigenvalues of a connected strongly regular graph. Let m1 = 1, m2 and m3 denote the multiplicity of r, λ2 and λ3, respectively. We here survey results related to the parameters n, r, τ and ???? for strongly regular graphs with m2 = qm3 and m3 = qm2 for q = 2,3,…,12.
Keywords:
Strongly regular graph, conference graph, integral graph.
References:
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