Spanning trees of dual graphs

Calculating the number of spanning trees

Calculating the number of spanning trees in a labeled planar molecular graph whose inner dual is a tree

✍ P. E. John; R. B. Mallion 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 496 KB 👁 3 views

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-

Graphs with all spanning trees nonisomor

Graphs with all spanning trees nonisomorphic

✍ Lars Døvling Andersen; Preben Dahl Vestergaard 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 487 KB

The paper presents some results on graphs that do not have two distinct isomorphic spanning trees. It is proved that any such connected graph with at least two vertices must have the property that each end-block has just one edge. On the other hand, the class of such graphs is quite large; it is sho

Graphs with homeomorphically irreducible

Graphs with homeomorphically irreducible spanning trees

✍ Michael O. Albertson; David M. Berman; Joan P. Hutchinson; Carsten Thomassen 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 509 KB

## Abstract It is an NP‐complete problem to decide whether a graph contains a spanning tree with no vertex of degree 2. We show that these homeomorphically irreducible spanning trees are contained in all graphs with minimum degree at least __c__√__n__ and in triangulations of the plane. They are ne

Graphs with certain families of spanning

Graphs with certain families of spanning trees

✍ P Erdös; R.J Faudree; C.C Rousseau; R.H Schelp 📂 Article 📅 1982 🏛 Elsevier Science 🌐 English ⚖ 510 KB

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