The smallest eigenvalue of Kr-free graphs
Abstract
Let G be a Kr+1-free graph with n vertices and m edges, and let λn(G) be the smallest eigenvalue of its adjacency matrix. We show thatλn(G)<-2r+1mr/rn2r-1.This implies also that if G is a d-regular graph of order n and independence number r, the second eigenvalue of G satisfiesλ2(G)≥-1+2/r(n-1-d)r/n r-1. © 2006 Elsevier B.V. All rights reserved.
Publication Title
Discrete Mathematics
Recommended Citation
Nikiforov, V. (2006). The smallest eigenvalue of Kr-free graphs. Discrete Mathematics, 306 (6), 612-616. https://doi.org/10.1016/j.disc.2006.01.014
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