Fortier Bourque, M. and Petri, B. (2019) Kissing numbers of regular graphs. arXiv, (Unpublished)
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200576.pdf - Submitted Version 984kB |
Publisher's URL: https://arxiv.org/abs/1909.12817
Abstract
We prove a sharp upper bound on the number of shortest cycles contained inside any connected graph in terms of its number of vertices, girth, and maximal degree. Equality holds only for Moore graphs, which gives a new characterization of these graphs. In the case of regular graphs, our result improves an inequality of Teo and Koh. We also show that a subsequence of the Ramanujan graphs of Lubotzky–Phillips–Sarnak have super-linear kissing numbers.
| Item Type: | Articles |
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| Status: | Unpublished |
| Refereed: | No |
| Glasgow Author(s) Enlighten ID: | Fortier-Bourque, Dr Maxime |
| Authors: | Fortier Bourque, M., and Petri, B. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | arXiv |
| Copyright Holders: | Copyright © 2019 The Authors |
| Publisher Policy: | Reproduced with the permission of the Author |
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