Undirected simple connected graphs with minimum number of spanning trees
โ Scribed by Zbigniew R. Bogdanowicz
- Book ID
- 108114075
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 765 KB
- Volume
- 309
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
proved that the spanning trees of a 2-cactus partition into at least 3 isomorphism classes. Here we examine the structure of these 2-cacti for which the spanning trees partition into exactly 3 isomorphism classes.
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 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