Naslov
Zigzags, Railroads, and Knots in Fullerenes

Autori
Deza, Michel ; Dutour, Mathieu ; Fowler, Patrick

Izvornik
Journal of chemical information and computer sciences (0095-2338) 44 (2004), 4; 1282-1293

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
plane graphs; zigzags; kekule structure

Sažetak
Two connections between fullerene structures and alternating knots are established. Knots may appear in two ways: from zig-zags, i.e. circuits (possibly self-intersecting) of edges running alternately left and right at successive vertices, and from railroads, i.e. circuits (possibly self-intersecting) of edge-sharing hexagonal faces, such that the shared edges occur in opposite pairs. A z-knot fullerene has only a single zig-zag, doubly covering all edges: in the range investigated (n <= 74) examples are found for C34 and all Cn with n >= 38, all chiral, belonging to groups C1, C2, C3, D3 or D5. An r-knot fullerene has a railroad corresponding to the projection of a non-trivial knot: examples are found for C52 (trefoil), C54 (figure-of-eight or Flemish knot) and, with isolated pentagons, at C96, C104, C108, C112, C114. Statistics on the occurrence of z-knots and of z-vectors of various kinds, z-uniform, z-transitive and z-balanced, are presented for trivalent polyhedra, general fullerenes and isolated-pentagon fullerenes, along with examples with self-intersecting railroads, and r-knots. In a subset of z-knot fullerenes, so-called minimal knots, the unique zig-zag defines a specific Kekule structure in which double bonds lie on lines of longitude and single bonds on lines of latitude of the approximate sphere defined by the polyhedron vertices.

Izvorni jezik
Engleski

Znanstvena područja
Kemija

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