AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
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Brandt [Discrete Math. 183 (1998) 17--25] conjectured that the least signless Laplacian eigenvalue of every regular triangle-free graph of order $n$ is at most $4n/25$. Using flag algebras, Balogh, Clemen, Lidick\'y, Norin and Volec [SIAM J. Discrete Math. 37 (2023) 1173--1179] established the stronger bound $15n/94$ f...
For a graph $G$ of order $n$, put $\sigma(G)=(\lambda_1(G)+\lambda_n(G))/n$. We determine the first three largest values of this invariant among nonbipartite distance-regular graphs of diameter three and odd girth at least seven. The unique maximizer is the folded $7$-cube, with value $1/32$; the unique second maximize...
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