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Does this undirected graph with 6 vertices and 9 undirected edges have a name? enter image description here I know a few names that are not right. It is not a complete graph because all the vertices are not connected. It is close to K3,3 the utility graph, but not quite (and not quite matters in graph theory :-)

This graph came up in my analysis of quaternion triple products.

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  • $\begingroup$ It is the complement of $K_3\sqcup K_3$, no? $\endgroup$ – Mariano Suárez-Álvarez Jun 16 '11 at 3:46
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This is exactly $K_{3,3}$. What makes you say it's only "close" to it? Can you spot two independent sets of 3 vertices each here? Once you see that, and given that there are 9 edges, it must be the complete bipartite graph on two sets of 3 vertices each.

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  • $\begingroup$ Yup, you are right, it is $K_{3,3}$ $\endgroup$ – sweetser Jun 16 '11 at 16:39
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Take two opposing vertices (the leftmost and rightmost will do). Now swap them and draw the resulting picture.

You should get a very clear $K_{3,3}$ as a result.

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  • $\begingroup$ Thanks, that was the picture I needed to see. $\endgroup$ – sweetser Jun 16 '11 at 16:44
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You can also think of it as the Harary graph $H_{3,6}$.

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