Revisiting two classical results on graph spectra
Abstract
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) If H is a proper subgraph of a connected graph G of order n and diameter D, then μ (G) - μ (H) > 1/μ (G)2dn. (ii) If G is a connected nonbipartite graph of order n and diameter D, then μ (G) + μmin (G) > 2/μ (G)2dn. For large μ and D these bounds are close to the best possible ones.
Publication Title
Electronic Journal of Combinatorics
Recommended Citation
Nikiforov, V. (2007). Revisiting two classical results on graph spectra. Electronic Journal of Combinatorics, 14 (1 R), 1-7. https://doi.org/10.37236/932
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