A survey on the missing Moore graph
View/Open
Issue date
20190116Suggested citation
Dalfó, Cristina;
.
(2019)
.
A survey on the missing Moore graph.
Linear Algebra and its Applications, 2019, vol. 569, p. 114.
https://doi.org/10.1016/j.laa.2018.12.035.
Metadata
Show full item recordAbstract
This is a survey on some known properties of the possible Moore graph (or graphs) ϒ 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 ϒ induced by a vertex subset C, the following graphs are distanceregular: 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 ϒ. Besides, ϒ is an edgedistanceregular graph.
Is part of
Linear Algebra and its Applications, 2019, vol. 569, p. 114European research projects
Collections
The following license files are associated with this item:
Related items
Showing items related by title, author, creator and subject.

The spectral excess theorem for graphs with few eigenvalues whose distance 2 or distance1or2 graph is strongly regular
Dalfó, Cristina; Fiol, Miguel Angel; Koolen, Jack (Taylor & Francis, 20180713)We study regular graphs whose distance2 graph or distance1or2 graph is strongly regular. We provide a characterization of such graphs Γ (among regular graphs with few distinct eigenvalues) in terms of the spectrum and ... 
On Middle Cube Graphs
Dalfó, Cristina; Fiol, Miguel Angel; Mitjana, Margarida (Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia, 2015)We study a family of graphs related to the $n$cube. The middle cube graph of parameter k is the subgraph of $Q_{2k1}$ induced by the set of vertices whose binary representation has either $k1$ or $k$ number of ones. The ... 
A general method to obtain the spectrum and local spectra of a graph from its regular partitions
Dalfó, Cristina; Fiol, Miguel Angel (International Linear Algebra Society, 20200712)It is well known that, in general, part of the spectrum of a graph can be obtained from the adjacency matrix of its quotient graph given by a regular partition. In this paper, a method that gives all the spectrum, and also ...