Interpolation theorem for diameters of spanning trees

Harary, Frank; Mokken, R.J.; Plantholt, M.

doi:10.1109/tcs.1983.1085385

Cited by 30 publications

(12 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Several variations of the tree graph have been studied; see for instance the adjacency tree graph studied by Zhang and Chen in [5] and by Heinrich and Liu in [3], and the leaf exchange tree graph of Broersma and Li [1] and Harary et al [2].…”

Section: Ap Figueroa and E Rivera-campomentioning

confidence: 99%

On the tree graph of a connected graph

Figueroa¹,

Rivera-Campo²

2008

Discuss. Math. Graph Theory

View full text Add to dashboard Cite

Let G be a graph and C be a set of cycles of G. The tree graph of G defined by C, is the graph T (G, C) that has one vertex for each spanning tree of G, in which two trees T and T are adjacent if their symmetric difference consists of two edges and the unique cycle contained in T ∪ T is an element of C. We give a necessary and sufficient condition for this graph to be connected for the case where every edge of G belongs to at most two cycles in C.

show abstract

Section: Ap Figueroa and E Rivera-campomentioning

confidence: 99%

On the tree graph of a connected graph

Figueroa¹,

Rivera-Campo²

2008

Discuss. Math. Graph Theory

View full text Add to dashboard Cite

show abstract

“…Given a connected graph G the (combinatorial) tree graph T ðGÞ is the graph whose vertices are the spanning trees of G and two trees P and Q are adjacent in T ðGÞ if there are edges e 2 P and f 2 Q such that Q ¼ P À e þ f . This graph has been widely studied as well as some of its variations, like the adjacency tree graph [10,16], the leaf exchange tree graph [2,7], the tree graph defined by a set of cycles [5,12] and the fixed degree tree graph [6], among others. Avis and Fukuda [1] studied the geometric version of the combinatorial problem: given a set P of points in general position, the graph T ðPÞ is the subgraph of T ðnÞ induced by the plane trees.…”

Section: Introductionmentioning

confidence: 99%

The biplanar tree graph

Figueroa

Fresán-Figueroa

2020

Bol. Soc. Mat. Mex.

View full text Add to dashboard Cite

The complete twisted graph of order n, denoted by T n , is a complete simple topological graph with vertices u 1 ; u 2 ;. . .; u n such that two edges u i u j and u i 0 u j 0 cross if and only if i\i 0 \j 0 \j or i 0 \i\j\j 0. The convex geometric complete graph of order n, denoted by G n , is a convex geometric graph with vertices v 1 ; v 2 ;. . .; v n placed counterclockwise, in which every pair of vertices is adjacent. A biplanar tree of order n is a labeled tree with vertex set fv 1 ; v 2 ;. . .; v n g having the property of being planar when embedded in both T n and G n. Given a connected graph G the (combinatorial) tree graph T ðGÞ is the graph whose vertices are the spanning trees of G and two trees P and Q are adjacent in T ðGÞ if there are edges e 2 P and f 2 Q such that Q ¼ P À e þ f. For all positive integers n, we denote by T ðnÞ the graph T ðK n Þ. The biplanar tree graph, BðnÞ, is the subgraph of T ðnÞ induced by the biplanar trees of order n. In this paper we give a characterization of the biplanar trees and we study the structure, the radius and the diameter of the biplanar tree graph.

show abstract

“…Some variations of the tree graph have been studied, like the adjacency tree graph studied by Zhang and Chen [11] and by Heinrich and Liu [8], the leaf exchange tree graph studied by Broersma and Li [3] and by Harary, Mokken and Plantholt [6]; and the tree graph defined by a set of cycles studied by Li, Neumann-Lara and Rivera-Campo [9].…”

Section: Introductionmentioning

confidence: 99%

On the Fixed Degree Tree Graph

Fresán-Figueroa

Rivera-Campo

2017

Journal of Information Processing

View full text Add to dashboard Cite

A 2-switch on a simple graph G consists of deleting two edges {u, v} and {x, y} of G and adding the edges {u, x} and {v, y}, provided the resulting graph is a simple graph. It is well known that if two graphs G and H have the same set of vertices and the same degree sequence, then H can be obtained from G by a finite sequence of 2-switches. While the 2-switch transformation preserves the degree sequence other conditions like connectivity may be lost. We study the restricted case where 2-switches are applied to trees to obtain trees.

show abstract

Interpolation theorem for diameters of spanning trees

Cited by 30 publications

References 5 publications

On the tree graph of a connected graph

On the tree graph of a connected graph

The biplanar tree graph

On the Fixed Degree Tree Graph

Contact Info

Product

Resources

About