Dipole graph

In graph theory, a dipole graph (also called a dipole or bond graph) 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.

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

The honeycomb as an abstract graph is the maximal abelian covering graph of the dipole graph D₃, while the diamond crystal as an abstract graph is the maximal abelian covering graph of D₄.

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.