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

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

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, pp prezentacija, znanstveni

Izvornik
ISM symposium, Statistics combinatorics and geometry, The Institute of Statistical Mathematics / - , 2003

Skup
ISM symposium, Statistics combinatorics and geometry, The Institute of Statistical Mathematics

Mjesto i datum
Tokyo, Japan, 20.03.2003. - 22.03.2003

Vrsta sudjelovanja
Plenarno

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
plane graph; point groups; central circuit; irreducibility

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: * All i-hedrites, which are not 3-connected, are identified. * Any irreducible i-hedrite has at most i-2 central circuits. * All i-hedrites without self- intersecting central circuits are listed. * All symmetry group of i-hedrites are listed.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA