Equitability of Fused-Hexacyclic Systems

A special seminar in Chemical Graph Theory given by Martin Lewinter Purchase College (SUNY)

A perfect matching for a graph, G, is a set of edges, S, such that each vertex of G is incident with exactly one edge in S. In particular, if a hexacyclic graph, G, represents a benzenoid, a perfect matching corresponds to the location of double bonds (pi-bonds). We present a type of coronafusene termed cyclofusene, in which each hexacycle shares exactly two nonadjacent edges with other hexacycles. Cyclofusene has exactly four configurations of pi bonds such that each pi bond belongs to the inner or outer boundary. In each of these configurations, the outer boundary has six more pi bonds than the inner boundary. The number of shared pi bonds in any mixed configuration is even. Let m be the number of shared pi bonds in a mixed configuration for a cyclofusene with exactly k linear chains. Then m >= k. Furthermore, there exists a mixed configuration with exactly k shared pi bonds.

This talk will be accessible to undergraduate students.

Location 107 LOV 1:25-2:15 Friday 6 April 2007.