dipole graph

{{Short description|Multigraph with two vertices}}

{{No footnotes|date=November 2024}}

{{infobox graph

| name = Dipole graph

| image = 140px

| image_caption =

| vertices = 2

| edges = {{mvar|n}}

| chromatic_number = 2 (for {{math|n ≥ 1}})

| chromatic_index = {{mvar|n}}

| diameter = 1 (for {{math|n ≥ 1}})

| properties = connected (for {{math|n ≥ 1}})
planar

}}

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 {{mvar|n}} edges is called the {{nowrap|size-{{mvar|n}}}} dipole graph, and is denoted by {{math|D{{sub|n}}}}. The {{nowrap|size-{{mvar|n}}}} dipole graph is dual to the cycle graph {{math|C{{sub|n}}}}.

The honeycomb as an abstract graph is the maximal abelian covering graph of the dipole graph {{math|D{{sub|3}}}}, while the diamond crystal as an abstract graph is the maximal abelian covering graph of {{math|D{{sub|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.