Lin-Lu-Yau curvature and diameter of amply regular graphs

doi:10.52396/JUST-2021-0232

Journal of University of Science and Technology of China ›› 2021, Vol. 51 ›› Issue (12): 889-893.DOI: 10.52396/JUST-2021-0232

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Lin-Lu-Yau curvature and diameter of amply regular graphs

LI Xintian, LIU Shiping^*

School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China

Received:2021-11-09 Revised:2021-11-16 Online:2021-12-31 Published:2022-01-11
Contact: *E-mail: spliu@ustc.edu.cn

Abstract

Abstract: By Hall’s marriage theorem, we study lower bounds of the Lin-Lu-Yau curvature of amply regular graphs with girth 3 or 4 under different parameter restrictions.As a consequence,we show that each conference graph has positive Lin-Lu-Yau curvature.Our approach also provides a geometric proof of a known diameter estimates of amply regular graphs in the case of girth 4 and some special cases of girth 3.

Key words: amply regular graph, perfect matching, Wasserstein distance, Lin-Lu-Yau curvature

CLC Number:

LI Xintian, LIU Shiping. Lin-Lu-Yau curvature and diameter of amply regular graphs[J]. Journal of University of Science and Technology of China, 2021, 51(12): 889-893.

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Lin-Lu-Yau curvature and diameter of amply regular graphs

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