Revisiting Two Classical Results on Graph Spectra

@article{Nikiforov2007RevisitingTC,
  title={Revisiting Two Classical Results on Graph Spectra},
  author={Vladimir Nikiforov},
  journal={Electr. J. Comb.},
  year={2007},
  volume={14}
}
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) n . (ii) If G is a connected nonbipartite graph of order n and diameter D, then μ (G) + μmin (G) > 2 μ (G) n . For large μ and D these bounds are close to the best possible ones.