Graphs as rotations

Dainis Zeps (1)

1 IMCS - Institute of Mathematics and Computer Science

Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces. Further, we define multiplication of these objects, that coincides with the multiplication of permutations. We consider closed under multiplication classes of combinatorial maps that consist of closed classes of combinatorial maps with fixed edges where each such class is defined by a knot. One class among them is special, containing selfconjugate maps.

Mots clés: combinatorial maps; permutations; graphs on surface

Domaines: Combinatoire [math.CO]

Dainis Zeps. Graphs as rotations. 1996. ⟨hal-00411981⟩