# Name of a 6 vertices graph

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.

• It is the complement of $K_3\sqcup K_3$, no? – Mariano Suárez-Álvarez Jun 16 '11 at 3:46

## 3 Answers

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.

• Yup, you are right, it is $K_{3,3}$ – sweetser Jun 16 '11 at 16:39

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.

• Thanks, that was the picture I needed to see. – sweetser Jun 16 '11 at 16:44

You can also think of it as the Harary graph $H_{3,6}$.