Does this undirected graph with 6 vertices and 9 undirected edges have a name?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.
$\endgroup$ 13 Answers
$\begingroup$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.
$\endgroup$ 1 $\begingroup$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.
$\endgroup$ 1 $\begingroup$You can also think of it as the Harary graph $H_{3,6}$.
$\endgroup$
