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- W4287390711 abstract "Let $mu_1 ge ldots ge mu_n$ denote the eigenvalues of a graph $G$ with $m$ edges and clique number $omega(G)$. Nikiforov proved a spectral version of Tur'an's theorem that [ mu_1^2 le frac{2m(omega - 1)}{omega}, ] and Bollob'as and Nikiforov conjectured that for $G not = K_n$ [ mu_1^2 + mu_2^2 le frac{2m(omega - 1)}{omega}. ] This paper proposes the conjecture that for all graphs $(mu_1^2 + mu_2^2)$ in this inequality can be replaced by the sum of the squares of the $omega$ largest eigenvalues, provided they are positive. We prove the conjecture for weakly perfect, Kneser, Johnson and classes of strongly regular graphs. We also provide experimental evidence and describe how the bound can be applied." @default.
- W4287390711 created "2022-07-25" @default.
- W4287390711 creator A5026944306 @default.
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- W4287390711 date "2021-01-13" @default.
- W4287390711 modified "2023-09-30" @default.
- W4287390711 title "Generalising a conjecture due to Bollobas and Nikiforov" @default.
- W4287390711 doi "https://doi.org/10.48550/arxiv.2101.05229" @default.
- W4287390711 hasPublicationYear "2021" @default.
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