Talk:Moore graph

message: The given definition seems rather nonsensical to me. A cage graph is, by definition, regular, and a cage graph with a vertex degree of 2 would be foolishly trivial, but there is no need to exclude them. What the definition is lacking is either some restriction on the definition of cage graphs (that is, a Moore graph is a cage graph with the number of vertices not exceeding a certain limit, like it is done in Mathworld: http://mathworld.wolfram.com/MooreGraph.html), or alternatively, starting with some statement about the relationship between diameter and girth (like it is done in PlanetMath: http://planetmath.org/encyclopedia/MooreGraph.html), or preferably both, and showing that both definitions define the same. Marfisa 21:48, 17 July 2006 (UTC)
replies: text: Better now? —David Eppstein 00:48, 2 October 2006 (UTC)

text: Done. —David Eppstein 02:57, 16 August 2007 (UTC)
thread_title: Definition

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thread_title:  External links modified (February 2018) 

message: Hey everyone,
I found a paper that claims to prove non-existence of a 57-regular Moore graph with diameter 2. Check it out here: https://arxiv.org/abs/2010.13443 Nicolas0301 (talk) 22:04, 24 January 2023 (UTC)
replies: text: It is still unpublished, and another pre-print claims that there is an error in this proof: https://arxiv.org/abs/2210.09577 - Saung Tadashi (talk) 22:22, 24 January 2023 (UTC)
thread_title:  Proof of non-existence of 57-regular Moore graph with diameter 2 

message: The phrases "A hypothetical graph of diameter 2, girth 5, degree 57 and order 3250" and "the unknown one"  suggests that if there exists a graph with diameter 2, girth 5, and degree 57, then it is unique up to isomorphism. However, it is possible that there exists non-isomorphic such graphs. See https://mathoverflow.net/questions/455807/girth-5-graphs-with-diameter-2 David.wood.42 (talk) 04:19, 6 October 2023 (UTC)
replies: text: Fixed. McKay (talk) 06:29, 3 November 2023 (UTC)
thread_title:  uniqueness of diameter 2, girth 5, degree 57 graph 

message: This page defines a "Moore graph" to be a regular graph whose girth is more than twice its diameter. The complete graph on two vertices is regular, with diameter 1, and has girth infinity (according to the definition at https://en.wikipedia.org/wiki/Girth_(graph_theory) ). So I think we need to add "contains a cycle" to the definition of Moore graph. David.wood.42 (talk) 23:15, 30 October 2023 (UTC)
thread_title:  definition of Moore graph