# Talk:Universal vertex

This review is transcluded from Talk:Universal vertex/GA1. The edit link for this section can be used to add comments to the review.
Nominator: David Eppstein (talk · contribs) 01:03, 1 September 2024 (UTC)
Reviewer: Dedhert.Jr (talk · contribs) 10:57, 1 September 2024 (UTC)

Reviewing, although I am not an expert in graph theory but okay nevermind. Dedhert.Jr (talk) 10:57, 1 September 2024 (UTC)


### Comments
Are you supposed to add more pictures about those special families on each graph? It might be helpful for readers, but my thought is that they are unnecessarily important because of the image criteria of GA. Dedhert.Jr (talk) 13:13, 1 September 2024 (UTC)
"The trivially perfect graph...": Would you like to explain this too-technical parenthesis explanation and break this overlong? Hopefully, the footnote is beneficial to reduce the overlong explanation again. Dedhert.Jr (talk) 13:13, 1 September 2024 (UTC)
Do you have to explicitly say the authors for the friendship theorem? Also, correct me if I'm wrong but are linking both "friendship theorem" and "friendship graph" considered WP:DUPLINK, technically? Dedhert.Jr (talk) 13:13, 1 September 2024 (UTC)
Let me have a quick summary about the connection between a dismantled graph and a universal vertex: a graph is dismantled, roughly speaking, by removing some vertices; and when the graph is stopped being dismantled, the remaining vertices are the only ones that connect at a single vertex known as the universal vertex. Understandable, but wikilinking Neighborhood (graph theory)? Is it necessary to explain its alternative name, the cop-win graph? Footnoting it if affirmative? Dedhert.Jr (talk) 13:13, 1 September 2024 (UTC)
The "Recognition" section is like other properties of a universal vertex. Two wrapped questions:

Correct me if I am wrong, but isolated vertex should be the vertex that is not adjacent with other vertices at all, not a single one? And why is this equivalent to the universal vertex?
You already linked labeled graph, right?
Dedhert.Jr (talk) 13:13, 1 September 2024 (UTC)
Spot-checking references: the oldid of 1243358704

Larrion source is okay for the alternative terminology of "apex of the cone", although it says "cone with the apex 
  
    
      
        v
      
    
    {\displaystyle v}
  
".
"A course of the web graph" with a specific page labeled 7 does not include anything about the star graph having a dominating vertex. The wheel graph does. I feel like I understand a little bit after reading the definition of a star graph, but it seems the sources implicitly say about it. Would you like to explain?
"The Comparability Graph of a Tree" source says nothing about threshold graph, instead of proof of how to construct. Ditto reasoning and ditto question.
Pisanski source: ditto reason, but I understand this would imply the illustration of the wheel graph's definition itself. But no comments 'bout this.
Klee source is oou-kay.
Erdos source is okay, but I think their theorem's statement is somewhat implicit. It turns out that Chavatal & Kotzig, as an additional and secondary source, support it.
Bonato source supports the fact. Completely great.
Haynes source supports both facts. Completely great. [1]
Fisher source: Yeah, I don't mind it.
Lovasz source is okay, supported on page 9.
Sloane OEIS' source is okay.
Fomin source is okay, supported on page 3.
I think that's all for today. The article meets criteria of 2b, 2c, 3a and 3b. 4 and 5 are obviously no need to be questioned. 1a, 1b, 2a, and 6 are the remaining minor problems. The WP:EARWIG shows 3.8%, 2.9%, and 2.9% on each enumerated listed respectively [2]. The article is somewhat attracted my attention to do a review. Apologies for the wording above and I will swiftly respond. Dedhert.Jr (talk) 13:13, 1 September 2024 (UTC)

Some responses to the part prior to the reference check:
I added a new image showing four special classes of graphs with a universal vertex, in the "In special families of graphs" section. Expanded the definition of trivially perfect graphs and split into multiple sentences. Removed friendship theorem author names and left only the main link to friendship graph.
Re your summary of dismantlable graphs: No, these do not always have a universal vertex. For instance, every tree can be dismantled by removing one leaf at a time. Added link to neighborhood. Re "Is it necessary to explain its alternative name, the cop-win graph": I think it's necessary to mention, because that is the main name for this class of graphs. I don't think it's necessary to explain or footnote the rules of the game here.
Re "The "Recognition" section is like other properties of a universal vertex": these are properties specifically connected to algorithms. Your description of isolated vertices is correct; the definition was stated in the description of threshold graphs. Why equivalent: taking the complement graph changes universal to isolated and vice versa, without changing the numbers of graphs. That's why I wrote "or equivalently isolated, in the complement graph". Second link to labeled graph removed. —David Eppstein (talk) 00:19, 3 September 2024 (UTC)
Noted it. Please notify me if you have completed all of those. Dedhert.Jr (talk) 04:53, 3 September 2024 (UTC)
Oh okay. I think all of them are completed. I do not notice the source of Bonato says about the star graph. So, nevermind about the sources. Passing. Dedhert.Jr (talk) 05:05, 4 September 2024 (UTC)
Thanks! —David Eppstein (talk) 06:33, 4 September 2024 (UTC)