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 one 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.