More on graphs with just three distinct eigenvalues

Citation

Rowlinson P (2017) More on graphs with just three distinct eigenvalues. Applicable Analysis and Discrete Mathematics, 11, pp. 74-80. https://doi.org/10.2298/AADM161111033R

Abstract
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).

Journal
Applicable Analysis and Discrete Mathematics: Volume 11

People

Professor Peter Rowlinson

Emeritus Professor, Mathematics