The structure and unlabelled enumeration of toroidal graphs with no K3, 3's

We characterize the toroidal graphs with no K3,3-subdivisions as canonical compositions in which 2-pole planar networks are substituted for the edges of non-planar cores. This structure enables us to enumerate these graphs. We describe an explicit enumerative approach that requires unlabelled enumeration of 2-connected planar graphs.

• Type: Journal
• Year: 2006
• Where: ENDM
• Authors: Andrei Gagarin, Gilbert Labelle, Pierre Leroux
• Keywords: 2-connected Planar Graphs, 2-pole Planar Networks, ENDM 2006, Toroidal Graphs