Introduction to molecular Schläfli indices

Match

Volumn 54, Issue 1, 2005, Pages 121-136

  Bucknum, Michael J ^a   Castro, Eduardo A ^b  

^a GEORGIA COLLEGE AND STATE UNIVERSITY   (United States)

^b INSTITUTO DE INVESTIGACIONES FISICOQUÍMICAS TEÓRICAS Y APLICADAS INIFTA   (Argentina)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27544499294     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. Elementa doctrinae solidorum and Demonstratio nonnularum insignium proprietatum quibus solida heddris planis inclusa sunt praedita, L. Euler, included in the Proceedings of the St. Petersburg Academy, 1758.
2. A.F. Wells, Three Dimensional Nets and Polyhedra, 1st edition, John Wiley and Sons Inc., New York, 1977.
3. M. Henle, A Combinatorial Introduction to Topology, 1st Edition, W.H. Freeman and Company, San Francisco, CA, 1979, p. 9.
4. M.J. Bucknum, "Calculating Topological Indexes for a Network Based Upon the Wells Point Symbol for the Network", in preparation.
5. M.J. Bucknum, Carbon, 35, 1, (1997).
6. L. Euler, Comment Acad. Sci. Imp. Petropolitanae, 8, 128, (1736).
7. H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973.
8. L. Pauling, General Chemistry, 3rd edition, Dover, New York, 1988.
9. J. Baggott, Perfect Symmetry: The Accidental Discovery of Buckminsterfullerene, 1st edition, Oxford University Press, Oxford, U.K., 1996.
10. A.F. Wells, Structural Inorganic Chemistry, 4th edition, Oxford University Press, Oxford, U.K., 1984.
11. A.T. Balaban (ed.), Chemical Applications of Graph Theory, Academic Press, London, 1976.
12. Although the problem of computing the connectivity, p, of molecular graphs is straightforward, the complementary problem of computing a polygonality, n, of a molecular graph is, in many instances, complicated by structural considerations and their related polygonalization ambiguities. This paper is the first in what it is hoped will be a pair of papers clarifying the rules by which polygonalities of molecular graphs may be computed. Some rules to be addressed in the next paper include (1) the adjacency principle, which states that in cases of ambiguity, the polygonalization that results in the 1 connected atoms being connected to adjacent 1-connected atoms, for the molecular graph, takes precedence; and with (1) satisfied we have a second rule; (2) the parsimony principle, which states in cases of a polygonalization ambiguity, the polygonalization which minimizes the total number of polygons counted in the polygonalization procedure takes precedence.