# 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$.