121 citations · 538 across the 72 of their papers we have counts for
6 papers · 1 filter
Bakry-Émery calculus for entropic curvature, new diameter estimates, and spectral gaps
Supanat Kamtue, Shiping Liu, Florentin Münch +1
In this paper, we propose a generalization of Bakry-Émery's calculus which allows us to formulate both Bakry-Émery and entropic curvature simultaneously. This formulation represent…
New graph invariants based on -Laplacian eigenvalues
Chuanyuan Ge, Shiping Liu, Dong Zhang
We present monotonicity inequalities for certain functions involving eigenvalues of -Laplacians on signed graphs with respect to . Inspired by such monotonicity, we propose n…
On the nontrivial extremal eigenvalues of graphs
Wenbo Li, Shiping Liu
We present a finer quantitative version of an observation due to Breuillard, Green, Guralnick and Tao which tells that for finite non-bipartite Cayley graphs, once the nontrivial e…
Bakry-Émery and Ollivier Ricci Curvature of Cayley Graphs
David Cushing, Supanat Kamtue, Riikka Kangaslampi +3
In this article we study two discrete curvature notions, Bakry-Émery curvature and Ollivier Ricci curvature, on Cayley graphs. We introduce Right Angled Artin-Coxeter Hybrids (RAAC…
Vertex isoperimetry on signed graphs and spectra of non-bipartite Cayley and Cayley sum graphs
Chunyang Hu, Shiping Liu
For a non-bipartite finite Cayley graph, we show the non-trivial eigenvalues of its normalized adjacency matrix lie in the interval $$\left[-1+\frac{ch_{out}^2}{d},1-\frac{Ch_{out}…
Graph bundles and Ricci-flatness
Wenbo Li, Shiping Liu
We develop a systematical way of constructing S-Ricci flat graphs which are not Abelian Cayley via graph bundle with explicit examples. For this purpose, we prove that, with some n…