Calculating the number of spanning trees in a labeled planar molecular graph whose inner dual is a tree
✍ Scribed by P. E. John; R. B. Mallion
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 496 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0020-7608
No coin nor oath required. For personal study only.
✦ Synopsis
The quantum mechanical relevance of the concept of a spanning tree extant within a given molecular graph-specifically, one that may be considered to represent the carbon-atom connectivity of a particular (planar) conjugated system-was first explicitly pointed out by Professor Roy McWeeny in his now-classic 1958 memoire entitled "Ring Currents and Proton Magnetic Resonance in Aromatic Molecules." In a recent work, Gutman and one of the present authors proposed a scheme for calculating the number of spanning trees in the graph associated with catacondensed, benzenoid molecules which, by definition, contain rings of just the one size (six-membered); here, we present an algorithmic approach that enables the determination of the number of spanning trees in the molecular graph of any catacondensed system (which, in general, has rings of more than one size, and these may be of any size). An illustrative example is given, in which the algorithm devised is applied to a (hypothetical) pentacyclic catacondensed structure comprising a five-membered ring, a six-membered ring, a seven-membered ring, and two four-membered rings. 0 1996 John Wiley & Sons, Inc.
tron "ring-currents," which, classically, are consid-