A survey on the missing Moore graph
This is a survey on some known properties of the possible Moore graph (or graphs) ¿ with degree 57 and diameter 2. Moreover, we give some new results about it, such as the following. When we consider the distance partition of ¿ induced by a vertex subset C, the following graphs are distance-regular:...
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| Format: | article |
| Publication Date: | 2019 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/127212 |
| Online Access: | https://hdl.handle.net/2117/127212 https://dx.doi.org/10.1016/j.laa.2018.12.035 |
| Access Level: | Open access |
| Keyword: | Graph theory Matrices Moore graphs Distance-regular graph Outindependent graph Spectral graph theory Automorphisms Grafs, Teoria de Anàlisi combinatòria Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
| Summary: | This is a survey on some known properties of the possible Moore graph (or graphs) ¿ with degree 57 and diameter 2. Moreover, we give some new results about it, such as the following. When we consider the distance partition of ¿ induced by a vertex subset C, the following graphs are distance-regular: The induced graph of the vertices at distance 1 from C when C is a set of 400 independent vertices; the induced graphs of the vertices at distance 2 from C when C is a vertex or an edge, and the line graph of ¿. Besides, ¿ is an edge-distance-regular graph. |
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