The Spectral Radius of Subgraphs of Regular Graphs

Let µ (G) and µmin (G) be the largest and smallest eigenvalues of the adjacency matrix of a graph G. Our main results are: (i) Let G be a regular graph of order n and finite diameter D. If H is a proper subgraph of G, then µ (G) − µ (H) > 1 nD . (ii) If G is a regular nonbipartite graph of order n and finite diameter D, then µ (G) + µmin (G) > 1 nD .

• Type: Journal
• Year: 2007
• Where: COMBINATORICS
• Authors: Vladimir Nikiforov
• Keywords: Adjacency Matrix, COMBINATORICS 2007, Graph G, Smallest Eigenvalues