Abstract
An inequality for superharmonic functions on Riemannian manifolds due to S.Y. Cheng and S-T. Yau is adapted to the setting of graphs. A number of corollaries are discussed, including a Harnack inequality for graphs having at most quadratic growth and satisfying a certain connectedness condition.
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Saloff-Coste, L. Some Inequalities for Superharmonic Functions on Graphs. Potential Analysis 6, 163–181 (1997). https://doi.org/10.1023/A:1008648421123
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DOI: https://doi.org/10.1023/A:1008648421123