An improved Moore bound and some new optimal families of mixed Abelian Cayley graphs
We consider the case in which mixed graphs (with both directed and undirected edges) are Cayley graphs of Abelian groups. In this case, some Moore bounds were derived for the maximum number of vertices that such graphs can attain. We first show these bounds can be improved if we know more details ab...
| Authors: | ; ; ; |
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| Format: | Article |
| Status: | Accepted version |
| Publication date: | 2020 |
| Country: | España |
| Institution: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repository: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10459.1/69173 |
| Online Access: | https://doi.org/10.1016/j.disc.2020.112034 http://hdl.handle.net/10459.1/69173 |
| Access Level: | Open access |
| Keyword: | Mixed graph Degree/diameter problem Moore bound |
| Summary: | We consider the case in which mixed graphs (with both directed and undirected edges) are Cayley graphs of Abelian groups. In this case, some Moore bounds were derived for the maximum number of vertices that such graphs can attain. We first show these bounds can be improved if we know more details about the order of some elements of the generating set. Based on these improvements, we present some new families of mixed graphs. For every fixed value of the degree, these families have an asymptotically large number of vertices as the diameter increases. In some cases, the results obtained are shown to be optimal. |
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