1 citations · 1 across the 2 of their papers we have counts for
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math.CO2020
An Alon-Boppana theorem for powered graphs and generalized Ramanujan graphs
Emmanuel Abbe, Peter Ralli
The r-th power of a graph modifies a graph by connecting every vertex pair within distance r. This paper gives a generalization of the Alon-Boppana Theorem for the r-th power of gr…
math.CO2018
Volume growth, curvature, and Buser-type inequalities in graphs
Brian Benson, Peter Ralli, Prasad Tetali
We study the volume growth of metric balls as a function of the radius in discrete spaces, and focus on the relationship between volume growth and discrete curvature. We improve vo…
math.CO2017★ 1 cited
Bounds on curvature in regular graphs
Peter Ralli
We study the curvature-dimension inequality in regular graphs. We develop techniques for calculating the curvature of such graphs, and we give characterizations of classes of graph…