# Maxima of the Q-index: Forbidden even cycles

## Abstract

Let G be a graph of order n and let q(G) be the largest eigenvalue of the signless Laplacian of G. Let Sn,k be the graph obtained by joining each vertex of a complete graph of order k to each vertex of an independent set of order n-k; let Sn,k+ be the graph obtained by adding an edge to Sn,k. It is shown that if k ≥2≤, n≥400k2, and G is a graph of order n, with no cycle of length 2k+2, then q(G)

## Publication Title

Linear Algebra and Its Applications

## Recommended Citation

Nikiforov, V., & Yuan, X.
(2015). Maxima of the Q-index: Forbidden even cycles.* Linear Algebra and Its Applications**, 471*, 636-653.
https://doi.org/10.1016/j.laa.2015.01.019