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
A new technique for the characterization of graphs with a maximum number of spanning trees
โ Scribed by L. Petingi; J. Rodriguez
- Book ID
- 108315634
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 203 KB
- Volume
- 244
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
๐ 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
In this paper, we present some sharp upper bounds for the number of spanning trees of a connected graph in terms of its structural parameters such as the number of vertices, the number of edges, maximum vertex degree, minimum vertex degree, connectivity and chromatic number.