New family of small regular graphs of girth 5
A (k, g)-cage is a k-regular graph of girth g of minimum order. In this work, we focus on girth g = 5, where cages are known only for degrees k ≤ 7. When k ≥ 8, except perhaps for k = 57, the order of a (k, 5)-cage is strictly greater than 1 + k2. Considering the relationship between finite geometri...
| Authors: | , , , |
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| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2016 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/163711 |
| Online Access: | https://hdl.handle.net/11441/163711 https://doi.org/10.1016/j.endm.2016.09.025 |
| Access Level: | Open access |
| Keyword: | Regular graph Cage Girth Amalgam |
| Summary: | A (k, g)-cage is a k-regular graph of girth g of minimum order. In this work, we focus on girth g = 5, where cages are known only for degrees k ≤ 7. When k ≥ 8, except perhaps for k = 57, the order of a (k, 5)-cage is strictly greater than 1 + k2. Considering the relationship between finite geometries and graphs we establish upper constructive bounds that improve the best so far. |
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