Naslov
4-valent plane graphs with 2-, 3- and 4-gonal faces

Autori
Deza, Michel ; Dutour, Mathieu ; Shtogrin, Mikhail

Vrsta, podvrsta i kategorija rada
Poglavlja u knjigama, znanstveni

Knjiga
Advances in Algebra: Proceedings of the Icm Satellite Conference in Algebra and Related Topics

Urednik/ci
Shum K.P.

Izdavač
World Scientific Publishing

Grad
Singapur

Godina
2003

Raspon stranica
73-97

ISBN
981-238-260-7

Ključne riječi
graphs, central circuits, reduction

Sažetak
Call i-hedrite any 4-valent n-vertex plane graph, whose faces are 2-, 3- and 4-gons only and p2+p3=i. The edges of an i-hedrite, as of any Eulerian plane graph, are partitioned by its central circuits, i.e. those, which are obtained by starting with an edge and continuing at each vertex by the edge opposite the entering one. So, any i-hedrite is a projection of an alternating link, whose components correspond to its central circuits. Call an i-hedrite irreducible, if it has no rail-road, i.e. a circuit of 4-gonal faces, in which every 4-gon is adjacent to two of its neighbors on opposite edges. We present the list of all i-hedrites with at most 15 vertices. Examples of other results: (i) All i-hedrites, which are not 3-connected, are identified. (ii) Any irreducible i-hedrite has at most i-2 central circuits. (iii) All i-hedrites without self-intersecting central circuits are listed. (iv) All symmetry group of i-hedrites are listed.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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