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Condensed Ricci
curvature on Paley graphs and their generalizations
Vincent Bonini, Daniel Chamberlin, Stephen Cook, Parthiv Seetharaman and Tri Tran |
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Vol. 19 (2026), No. 1, 161–179
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Abstract |
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We explore properties of generalized Paley graphs, and we extend a result of Lim and Praeger (Michigan Math. J. 58:1 (2009), 293–308) by providing a more precise description of the connected components of disconnected generalized Paley graphs. This result leads to a new characterization of generalized Paley graphs that are disconnected. We also provide necessary and sufficient divisibility conditions for the multiplicative group of the prime subfield of certain finite fields to be contained in the multiplicative subgroup of nonzero -th powers. This latter result plays a crucial role in our development of a sorting algorithm on generalized Paley graphs that exploits the vector space structure of finite fields to partition certain subsets of vertices in a manner that decomposes the induced bipartite subgraph between them into complete balanced bipartite subgraphs. As a consequence, we establish a matching condition between these subsets of vertices that results in an explicit formula for the condensed Ricci curvature on certain Paley graphs and their generalizations. |
Keywords
coarse Ricci curvature, Ricci curvature on graphs, Paley
graphs, generalized Paley graphs, complete subgraphs
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Mathematical Subject Classification
Primary: 52C99, 53B99
Secondary: 05C10, 05C81, 05C99
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Milestones
Received: 21 July 2024
Revised: 30 August 2024
Accepted: 2 September 2024
Published: 25 January 2026
Communicated by Anant Godbole
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Authors |
| Vincent Bonini | |
| Mathematics Department California Polytechnic State University San Luis Obispo, CA United States |
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| Daniel Chamberlin | |
| Mathematics Department California Polytechnic State University San Luis Obispo, CA United States |
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| Stephen Cook | |
| Mathematics Department California Polytechnic State University San Luis Obispo, CA United States |
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| Parthiv Seetharaman | |
| Mathematics Department California Polytechnic State University San Luis Obispo, CA United States |
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| Tri Tran | |
| Mathematics Department California Polytechnic State University San Luis Obispo, CA United States |
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| © 2026 MSP (Mathematical Sciences Publishers). |
