The signless Laplacian spectral radius of graphs without intersecting odd cycles

Let Fa1,...,ak be a graph consisting of k cycles of odd length 2a1 + 1, . . . , 2ak + 1, respectively which intersect in exactly a common vertex, where k ≥ 1 and a1 ≥ a2 ≥ · · · ≥ ak ≥ 1. In this paper, we present a sharp upper bound for the signless Laplacian spectral radius of all Fa1,...,ak -free graphs and characterize all extremal graphs which attain the bound. The stability methods and structure of graphs associated with the eigenvalue are adapted for the proof. AMS Classification: 05C50, 05C35

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