# moore graph

Published articles for moore graph.

This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles.

## A Spectral Analysis of Moore Graphs

DevFeed: [A Spectral Analysis of Moore Graphs](<https://devfeed.tech/articles/a-spectral-analysis-of-moore-graphs-40406.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2016/11/03/a-spectral-analysis-of-moore-graphs/>)

Published: 2016-11-03T08:00:14Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Graphs](<https://devfeed.tech/topics/graphs.md>)

Tags: [adjacency-matrix](<https://devfeed.tech/tags/adjacency-matrix.md>), [eigenvalues](<https://devfeed.tech/tags/eigenvalues.md>), [eigenvectors](<https://devfeed.tech/tags/eigenvectors.md>), [graph](<https://devfeed.tech/tags/graph.md>), [graphs](<https://devfeed.tech/tags/graphs.md>), [math](<https://devfeed.tech/tags/math.md>), [matrix](<https://devfeed.tech/tags/matrix.md>), [moore-graph](<https://devfeed.tech/tags/moore-graph.md>), [orthogonality](<https://devfeed.tech/tags/orthogonality.md>), [regular](<https://devfeed.tech/tags/regular.md>), [spectral-graph-theory](<https://devfeed.tech/tags/spectral-graph-theory.md>), [trace](<https://devfeed.tech/tags/trace.md>), [vertex](<https://devfeed.tech/tags/vertex.md>)

### AI overview

This mathematical article analyzes Moore graphs of girth 5 using the eigenvalues of their adjacency matrices. It derives the minimum vertex count and shows that the degree must be one of 3, 7, or 57.

### Source excerpt

For fixed integers $ r > 0$, and odd $ g$, a Moore graph is an $ r$-regular graph of girth $ g$ which has the minimum number of vertices $ n$ among all such graphs with the same regularity and girth. (Recall, A the girth of a graph is the length of its shortest cycle, and it's regular if all its vertices have the same degree) Problem (Hoffman-Singleton): Find a useful constraint on the relationship between $ n$ and $ r$ for Moore graphs of girth $ 5$ and degree $ r$.