On Characterizations of Rigid Graphs in the Plane Using Spanning Trees
โ Scribed by Sergey Bereg
- Publisher
- Springer Japan
- Year
- 2009
- Tongue
- English
- Weight
- 145 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0911-0119
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๐ SIMILAR VOLUMES
A graph G with n nodes and e edges is said to be t-optimal if G has the maximum number of spanning trees among all graphs with the same number of nodes and edges as G. Hitherto, t-optimal graphs have been characterized for the following cases: (a) n=sp, and e=(s(s-1)/2)p 2, when s and p are positive
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
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.