On maximally distant spanning trees of a graph

Maximizing spanning trees in almost comp

Maximizing spanning trees in almost complete graphs

✍ Gilbert, Bryan; Myrvold, Wendy 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 94 KB 👁 2 views

We examine the family of graphs whose complements are a union of paths and cycles and develop a very simple algebraic technique for comparing the number of spanning trees. With our algebra, we can obtain a simple proof of a result of Kel'mans that evening out path lengths increases the number of spa

Maximizing spanning trees in almost comp

Maximizing spanning trees in almost complete graphs

✍ Gilbert, Bryan; Myrvold, Wendy 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 94 KB 👁 2 views

We examine the family of graphs whose complements are a union of paths and cycles and develop a very simple algebraic technique for comparing the number of spanning trees. With our algebra, we can obtain a simple proof of a result of Kel'mans that evening-out path lengths increases the number of spa

On spanning 2-trees in a graph

✍ Leizhen Cai 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 963 KB

A k-tree is either a complete graph on k vertices or a graph T that contains a vertex whose neighbourhood in T induces a complete graph on k vertices and whose removal results in a k-tree. A subgraph of a graph is a spanning k-tree if it is a k-tree and contains every vertex of the graph. This pape

The number of spanning trees of a graph

✍ Jianxi Li; Wai Chee Shiu; An Chang 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 387 KB

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.

On the number of spanning trees in a mol

On the number of spanning trees in a molecular graph

✍ R.B. Mallion 📂 Article 📅 1975 🏛 Elsevier Science 🌐 English ⚖ 444 KB

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.

Spanning trees fixed by automorphisms of

Spanning trees fixed by automorphisms of a graph

✍ M. Kano; A. Sakamoto 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 223 KB

Let G be a finite graph and A be a subgroup of Aut(G). We give a necessary and sufficient condition for the graph G to have an A-invariant spanning tree.