On the number of spanning trees in a molecular graph
β Scribed by R.B. Mallion
- Publisher
- Elsevier Science
- Year
- 1975
- Tongue
- English
- Weight
- 444 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0009-2614
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β¦ Synopsis
A rccenl theorem due to W'aller is applied to the mokculnr gmph of a typical conjugtcd system (naphthalene) in order to demonstrate the enumeration of spanning trees, on each of which a "ring current" calculation may be based.
π SIMILAR VOLUMES
Let 3:; denote the set of simple graphs with n vertices and m edges, t ( G ) the number of spanning trees of a graph G , and F 2 H if t(K,\E(F))?t(K,\E(H)) for every s? max{u(F), u ( H ) } . We give a complete characterization of >-maximal (maximum) graphs in 3:; subject to m 5 n . This result conta
The problem is to determine the linear graph that has the maximum number of spanning trees, where only the number of nodes N and the number of branches B are prescribed. We deal with connected graphs G(N, B) obtained by deleting D branches from a complete graph KN. Our solution is for D less than or
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-
For a connected graph G, let ~-(G) be the set of all spanning trees of G and let nd(G) be the number of vertices of maximum degree in G. In this paper we show that if G is a cactus or a connected graph with p vertices and p+ 1 edges, then the set {na(T) : T C ~-(G)) has at most one gap, that is, it
## Abstract The theorem of Gutman et al. (1983) is applied to calculate the number of spanning trees in the carbonβcarbon connectivityβnetwork of the recently diagnosed C~60~βcluster buckminsterfullerene. This βcomplexityβ turns out to be approximately 3.75 Γ 10^20^ and it is found necessary to inv