Barbell graph

In the mathematical discipline of graph theory, the n-barbell graph is a special type of undirected graph consisting of two non-overlapping n-vertex cliques together with a single edge that has an endpoint in each clique.[1]

Barbell graph
A barbell graph on 16 vertices.
Vertices	${\displaystyle 2n}$
Edges	${\displaystyle 2\cdot {\tbinom {n}{2}}+1}$
Properties	connected
Table of graphs and parameters