Non-derivable strongly regular graphs from quasi-symmetric designs

Pawale, Rajendra M.; Shrikhande, Mohan S.; Nyayate, Shubhada M.

doi:10.1016/j.disc.2015.09.017

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Cited by 4 publications

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“…By Theorem 3.1 such a graph exists if and only if there exists a quasi-symmetric (225, 400, 64, 36, 10)-design D. Then G 1 , the block graph of D, is strongly regular with parameters 400, 378, 357, 360; according to [2], the existence of such a strongly regular graph is unknown. We note that the parameters of G 1 and D satisfy the four necessary conditions for the existence of D formulated in [13,Theorem 6].…”

Section: Further Remarksmentioning

confidence: 99%

More on graphs with just three distinct eigenvalues

Rowlinson

2017

APPL ANAL DISCRETE M

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In honour of Dragoš Cvetković on the occasion of his 75th birthday.Let G be a connected non-regular non-bipartite graph whose adjacency matrix has spectrum ρ, µ (k) , λ (l) , where k, l ∈ IN and ρ > µ > λ. We show that if µ is non-main then δ(G) ≥ 1 + µ − λµ, with equality if and only if G is of one of three types, derived from a strongly regular graph, a symmetric design or a quasi-symmetric design (with appropriate parameters in each case).

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Section: Further Remarksmentioning

confidence: 99%