Talk:Moore graph

Definition
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)


 * Better now? —David Eppstein 00:48, 2 October 2006 (UTC)

The section Moore graphs as Cages needs to be fixed I think. When talking about the LHS of the equation for graphs of even girth, they mean RHS and vice versa. Bullery 21:52, 15 August 2007 (UTC)


 * Done. —David Eppstein 02:57, 16 August 2007 (UTC)

As cage
This phrase in the intro sounds like a theorem, rather than a summary of what is in the article, therefore there must be a clear indication where it comes from. It is alo unclear why this particular fact must be in the intro, which is a summary of the article, and should not contain factoids. Another approach is to rephrase this sentence into an intro phrase about the corresponding section. Twri (talk) 04:09, 23 February 2010 (UTC)


 * It comes from the section entitled "Moore graphs as cages". In what way is that not obvious? —David Eppstein (talk) 04:26, 23 February 2010 (UTC)
 * Your recent edits make me think that you already know the answer. Twri (talk) 05:37, 24 February 2010 (UTC)
 * No, I don't. Your calling attention to the article made me notice some issues with it that I addressed (who should get priority for observing that Moore graphs are cages, and fixing a typo where it said diameter and should have said girth). But I still don't understand what you were thinking for calling out a sentence in the lede as needing additional justification within the lede, when the subject of the sentence was very obviously the same as the subject of one of the whole sections of the article where the detail and justification would more naturally fit. The purpose of a lede is to summarize what's going to appear later, it's not to provide detail and sourcing itself, so your request for a source there seems to be counter to the spirit of WP:LEDE. I added the source there anyway, as well as in the later section where it belonged, not because I think it's a good idea for the sourcing to be placed there, but because I didn't want to get into an annoying edit war with you over something minor. —David Eppstein (talk) 21:19, 24 February 2010 (UTC)
 * OK. Here is an explanation. In addition to adding source, you fixed an error in the statement. While I have some knowledge in some aspects in graph theory, I am not an expert in all of it. I tried to read the statement and could not explain/verify it, neither by my own brain, nor after reading the article. Wasting no more brainpower, I suspected this was a yet another equivalent definition which I am failing to figure out, and requested a citation, for verification from the source. Since the phrase turned out to be a false statement (not merely "typo", as you say), your arguments are inapplicable.
 * Also, please allow me to repeat, even in the fixed form this sentence does not sound like a summary of the section "Moore graphs as cages". It is just a mathematical statement, with no stated implications ("they are cages... ... Well, good for them."). In order for a reader to expect more, it should be phrased like, e.g., "...therefore, Moore graphs are cages, and this gives additional insights into their properties.", or some other summarizing phrase. Twri (talk) 08:51, 25 February 2010 (UTC)

External links modified (February 2018)
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Proof of non-existence of 57-regular Moore graph with diameter 2
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)


 * 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)

uniqueness of diameter 2, girth 5, degree 57 graph
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)
 * Fixed. McKay (talk) 06:29, 3 November 2023 (UTC)

definition of Moore graph
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)