Is the image provided for a Cayley Diagram of $D_{4}$ in Wikimedia Commons wrong?

The image there seems to have the "outer ring" flipped:

enter image description here

Shouldn't this look more like this:

enter image description here

  • Your link points to the Cayley diagram of $D_4$, not $V_4$. – Mariano Suárez-Álvarez May 19 '12 at 4:21
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    In this diagram, the red arrow corresponds to multipication by $a$ on the left; your diagram is making it correspond to multiplication by $a$ on the right. So a red arrow that starts at $b$ should point to $ab$. Both conventions are okay, but it is true that the convention of the diagram clashes with the convention of the text. But the description in the text is accurate, as it identifies red arrows as "left multiplication by $a$". – Arturo Magidin May 19 '12 at 4:22
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    @raxacoricofallapatorius: In Group Theory, you will often find that all lateral conventions occur; some people like left actions, some people like right actions. Some people have homomorphisms on the left, some on the right. Some people define commutators by $[x,y]=x^{-1}y^{-1}xy$, some by $[x,y]=xyx^{-1}y^{-1}$. Etc. – Arturo Magidin May 19 '12 at 4:35
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    @raxacoricofallapatorius: In the article on Cayley graphs. The definition (Definition section) agrees that an arrow labeled $s$ goes from $g$ to $gs$. But in the Examples section, the fourth example (which describes this particular graph), it explicitly states "Red arrows represent left-multiplication by element $a$." – Arturo Magidin May 19 '12 at 18:45
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    @raxacoricofallapatorius: Not that I am aware of; there really is no essential problem attached to this issue, since any argument that uses one convention can be done, mutatis mutandis, using the other convention. I think the article on Cayley graphs is a bit of a problem because it uses one definition and then has an example using the other convention, but I haven't taken the time to bring it up in the talk page (perhaps you can). – Arturo Magidin May 19 '12 at 21:14
up vote 3 down vote accepted

In the Wikipedia diagram, the red arrow corresponds to multipication by $a$ on the left; your diagram is making it correspond to multiplication by $a$ on the right. Both conventions are okay, but it is true that the convention of the diagram clashes with the convention of the text.

  • Adapted from comments above. – orome Sep 6 '12 at 1:02

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