The paper proves the localized bound q(G) ≤ 2 ∑_v (1 − 1/c(v)) on the signless Laplacian spectral radius, where c(v) is the size of the largest clique containing vertex v, with equality cases for certain complete multipartite graphs.
An edge-spectral Erd¨ os-Stone-Simonovits the- orem and its stability, 2025
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Localized Tur\'{a}n-type inequalities for $Q$-index
The paper proves the localized bound q(G) ≤ 2 ∑_v (1 − 1/c(v)) on the signless Laplacian spectral radius, where c(v) is the size of the largest clique containing vertex v, with equality cases for certain complete multipartite graphs.