Discrete Schrödinger operators on a graph

@article{Sy1992DiscreteSO,
  title={Discrete Schr{\"o}dinger operators on a graph},
  author={Polly W. Sy and Toshikazu Sunada},
  journal={Nagoya Mathematical Journal},
  year={1992},
  volume={125},
  pages={141-150}
}
In this paper, we study some spectral properties of the discrete Schrodinger operator = Δ + q defined on a locally finite connected graph with an automorphism group whose orbit space is a finite graph. The discrete Laplacian and its generalization have been explored from many different viewpoints (for instance, see [2] [4]). Our paper discusses the discrete analogue of the results on the bottom of the spectrum established by T. Kobayashi, K. Ono and T. Sunada [3] in the Riemannian-manifold… 
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