Dipole graph

Vertices	2
Edges	$n$
Diameter	1 (for $n \geq 1$ )
Chromatic number	2
Chromatic index	$n$
Properties	connected (for $n \geq 1$ ) planar
Table of graphs and parameters

In graph theory, a dipole graph, dipole, bond graph, or linkage, is a multigraph consisting of two vertices connected with a number of parallel edges. A dipole graph containing $n$ edges is called the order- $n$ dipole graph, and is denoted by $D n$ . The order- $n$ dipole graph is dual to the cycle graph $C n$ .

The honeycomb as an abstract graph is the maximal abelian covering graph of the dipole graph $D 3$ , while the diamond crystal as an abstract graph is the maximal abelian covering graph of $D 4$ .

Similarly to the Platonic graphs, the dipole graphs form the skeletons of the hosohedra. Their duals, the cycle graphs, form the skeletons of the dihedra.

References