Maxima of the Q-index: graphs without long paths

Vladimir Nikiforov, Xiying Yuan

Published 2013-08-20Version 1

This paper gives tight upper bound on the largest eigenvalue q(G) of the signless Laplacian of graphs with no paths of given order. The main ingredient of our proof is a stability result of its own interest, about graphs with large minimum degree and with no long paths. This result extends previous work of Ali and Staton.