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.
Bounds for the largest eigenvalue and sum of laplacian eigen- values of signed graphs
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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.