Naslov
On the complexity of platonic solids

Autori
Trinajstić, Nenad ; Nikolić, Sonja ; Mihalić, Zlatko

Izvornik
Glasnik na hemičarite i tehnolozite na Makedonija (0350-0136) 13 (1994), 2; 61-68

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

Ključne riječi
complexity ; convex polyhedron ; platonic solid ; spanning tree

Sažetak
The Platonic solids serve as very useful structural rnodels in chemistry. The tetrahedron is especially important Platonic solid because it is a key structural unit in organic chernistry and represents the basis of our understanding of structures, properties and reactivities of carbon cornpounds. As a cornplexity rneasure of Platonic solids, we used the number of spanning trees. They were calculated using formula based on the Laplacian spectrum of a molecular graph. Schlegel graphs are convenient graph-theoretical representations of the Platonic solids. The icosahedron and the dodecahedron possess the largest number of the spanning trees and thus they appear to be the most cornplex Platonic solids. However, sorne of their characteristics, e.g., the rnatching number or the Bertz information-theoretic index, predict the icosahedron to be the most cornplex Platonic solid while the other, e.g., the Z-index, preter the dodecahedron.

Izvorni jezik
Engleski

Znanstvena područja
Kemija

POVEZANOST RADA