| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4649303 | Discrete Mathematics | 2006 | 5 Pages |
Abstract
Let G be a Kr+1Kr+1-free graph with n vertices and m edges, and let λn(G)λn(G) be the smallest eigenvalue of its adjacency matrix. We show thatλn(G)<-2r+1mrrn2r-1.This implies also that if G is a d-regular graph of order n and independence number rr, the second eigenvalue of G satisfiesλ2(G)⩾-1+2r(n-1-d)rnr-1.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Vladimir Nikiforov,