Talk:Möbius ladder

Notation?

Hello,

Where does $M_{n}$ notation come from? Wolfram, for instance, would call the Wagner graph the $4$-Möbius ladder, while this article names it $M_{8}$.

Using a number the half the number of the vertices is consistent with for example Ladder graph and simplifies a number of polynomials.

I propose a ranaming to $ML_{n}$ like in some papers I have seen and taking the half of all quantities. --MathsPoetry (talk) 09:33, 8 February 2013 (UTC)

The M_n notation (with n being the number of vertices) comes from the first paper on these graphs, by Guy and Harary (1967). In their description of the graph (as an n-cycle with all long diagonals added) this is more natural than counting the number of diagonals. Certainly other notations have been used; for instance Biggs et al. use $T_{n}^{\#}$ where as in your proposal n is half the number of vertices, and Maharry uses V_n where n is the number of vertices. But I think sticking to the original notation is not a bad idea in this case. More generally, I think it is a very bad idea to use n, in the context of graph theory, to mean anything other than the number of vertices, because it is so ingrained in that usage. —David Eppstein (talk) 21:26, 14 February 2013 (UTC)

As you said, sources can be found for a variety of notations. So I guess the choice is up to us, in conformance with the least surprise principle of course.

I like how it's handled on the page for the dihedral group, where it says, "In geometry, $D_{n}$ refers to the symmetries of the n-gon, [...] in abstract algebra, $D_{2n}$ refers to this same dihedral group. The geometric convention is used in this article." Peterkagey (talk) 22:03, 28 March 2019 (UTC)

Using n for something else than the total number of vertices is at least common on Wikipedia, e.g. Ladder graph, Friendship graph, Star graph, etc.

I'll use $ML_{n}$ in the French article, because it makes all formulas simpler. --MathsPoetry (talk) 14:06, 17 February 2013 (UTC)

Colour-coded graphs clearer than SVG animation

The above views colour-coded to show equivalence

@David Eppstein: reverted my addition of this image,[incorrect allegation] which I feel is much clearer than the SVG animation. I'm normally a great proponent of SVG animations but I find the animation doesn't really add to understanding the equivalence of the two depictions.

Though I can see David's point that colours have special meaning in terms of graph colouring, I think mentioning colour code in the caption is clear enough that the intended meaning is to identify the vertices. If using different shapes instead works, let me know and I'll change the diagram.

Thanks,
cmɢʟee⎆τaʟκ 23:54, 23 October 2021 (UTC)

I did not revert your addition of this image. I removed the monochromatic image that it made obsolete. Pay more attention next time before falsely accusing me of misbehavior that I did not do. Also, your statement "colours have special meaning in terms of graph colouring" is a total misunderstanding of what I wrote, which was not about your use of colors, but about your use of the phrase color-coding. That phrase has a special meaning in terms of graph algorithms that has little or nothing to do with either graph coloring or the use of color in graph visualization. —David Eppstein (talk) 23:58, 23 October 2021 (UTC)

Apologies, @David Eppstein: I hastily misread the diff and should've paid more attention to the filename. Nevertheless, I don't class reversion in general misbehaviour; from your contributions, I can see that you want to make Wikipedia a better place and have good reasons when you revert. I see now what you meant by the term color-coding. My bad. Cheers, cmɢʟee⎆τaʟκ 00:22, 24 October 2021 (UTC)

diameter of the Möbius ladder

The diameter of the Möbius ladder is not 1. Only complete graphs have diameter 1. David.wood.42 (talk) 20:41, 2 October 2023 (UTC)

Removed; thanks, David! This mistake appears to have been added last June by User:OlliverWithDoubleL when he first created the infobox. I imagine the correct diameter should be something like $n/4$ but to avoid WP:OR we should look for a published source for it rather than trying to figure it out ourselves, before adding it. —David Eppstein (talk) 21:24, 2 October 2023 (UTC)

@David.wood.42:

@David Eppstein:

Thank you both for catching my mistake. My apologies for the confusion; I'm not an expert in this subject and it wasn't my place to mess with it. My memory of making edits around that time is rather fuzzy, but I believe I also made a similar edit to another article on graph families, and I might have made a similar mistake there as well. I'll go through my edit history and try to fix any other OR from that time OlliverWithDoubleL (talk) 22:05, 4 October 2023 (UTC)