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.
Electronic Journal of Combinatorics
Nikiforov, V. (2007). The spectral radius of subgraphs of regular graphs. Electronic Journal of Combinatorics, 14 (1 N), 1-4. https://doi.org/10.37236/1021