The signless Laplacian spectral radius of graphs without intersecting odd cycles

Ming-Zhu Chen; A-Ming Liu; Xiao-Dong Zhang

paper

The signless Laplacian spectral radius of graphs without intersecting odd cycles

arXiv:2108.03895

Abstract

Let $F_{a_{1}, \dots, a_{k}}$ be a graph consisting of $k$ cycles of odd length $2 a_{1} + 1, \dots, 2 a_{k} + 1$ , respectively which intersect in exactly a common vertex, where $k \geq 1$ and $a_{1} \geq a_{2} \geq \dots \geq a_{k} \geq 1$ . In this paper, we present a sharp upper bound for the signless Laplacian spectral radius of all $F_{a_{1}, \dots, a_{k}}$ -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.

11 pages