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A survey on the missing Moore graph

Author: Dalfo, C.

Type of activity: Journal article
Journal: Linear algebra and its applications
Date of publication: 2019
Volume: 569
First page: 1
Last page: 14
DOI: https://doi.org/10.1016/j.laa.2018.12.035

Repository: http://hdl.handle.net/2117/127212
URL: https://www.sciencedirect.com/science/article/abs/pii/S0024379519300138
Abstract: 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 li...

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.
Citation: Dalfo, C. A survey on the missing Moore graph. "Linear algebra and its applications", 2019, vol. 569, p. 1-14.
Keywords: Automorphisms, Distance-regular graph, Moore graphs, Outindependent graph, Spectral graph theory

Group of research: COMBGRAPH - Combinatorics, Graph Theory and Applications

Participants

Dalfo Simo, Cristina (author)

Attachments

monster(18oct2017-rev30dec2018).pdf (373944 bytes)