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Constructing Independent Spanning Trees on Generalized Recursive Circulant Graphs

IEEE Access, 2021
The generalized recursive circulant networking can be widely used in the design and implementation of interconnection networks. It consists of a series of processors, each is connected through bidirectional, point-to-point communication channels to ...
Dun-Wei Cheng, Kai-Hsun Yao, Sun-Yuan Hsieh   +2 more
doaj   +1 more source

Spanning trees for many different numbers of leaves [PDF]

Discrete Mathematics & Theoretical Computer Science
Let $G$ be a connected graph and $L(G)$ the set of all integers $k$ such that $G$ contains a spanning tree with exactly $k$ leaves. We show that for a connected graph $G$, the set $L(G)$ is contiguous.
Kenta Noguchi, Carol T. Zamfirescu
doaj   +1 more source

Rooted Uniform Monotone Minimum Spanning Trees

, 2017
We study the construction of the minimum cost spanning geometric graph of a given rooted point set $P$ where each point of $P$ is connected to the root by a path that satisfies a given property.
Mastakas, Konstantinos, Symvonis, Antonios   +1 more
core   +1 more source

An Edge-Swap Heuristic for Finding Dense Spanning Trees

Theory and Applications of Graphs, 2016
Finding spanning trees under various restrictions has been an interesting question to researchers. A "dense" tree, from a graph theoretical point of view, has small total distances between vertices and large number of substructures.
Mustafa Ozen, Hua Wang, Kai Wang, Demet Yalman   +3 more
doaj   +1 more source

Spanning trees of 3-uniform hypergraphs [PDF]

, 2010
Masbaum and Vaintrob's "Pfaffian matrix tree theorem" implies that counting spanning trees of a 3-uniform hypergraph (abbreviated to 3-graph) can be done in polynomial time for a class of "3-Pfaffian" 3-graphs, comparable to and related to the class of ...
Andrew Goodall, Anna, De Mier
core  

Galactic Archaeology and Minimum Spanning Trees [PDF]

, 2015
Chemical tagging of stellar debris from disrupted open clusters and associations underpins the science cases for next-generation multi-object spectroscopic surveys.
Flynn, C.M.L., Gibson, Bradley Kenneth, macfarlane, B.A.   +2 more
core  

A formula for the number of spanning trees in circulant graphs with non-fixed generators and discrete tori

, 2015
We consider the number of spanning trees in circulant graphs of $\beta n$ vertices with generators depending linearly on $n$. The matrix tree theorem gives a closed formula of $\beta n$ factors, while we derive a formula of $\beta-1$ factors.
Louis, Justine
core   +1 more source

Computing Well-Balanced Spanning Trees of Unweighted Networks

Algorithms
A spanning tree of a network or graph is a subgraph that connects all nodes with the minimum number or total weight of edges. Spanning trees are among the simplest yet most effective techniques for network simplification, sampling, and uncovering a ...
Lovro Šubelj
doaj   +1 more source

The Maximum Distance Problem and Minimum Spanning Trees

International Journal of Analysis and Applications, 2021
Given a compact E⊂Rn and s>0, the maximum distance problem seeks a compact and connected subset of Rn of smallest one dimensional Hausdorff measure whose s-neighborhood covers E.
Enrique G. Alvarado, Bala Krishnamoorthy, Kevin R. Vixie   +2 more
doaj  

On the Number of Spanning Trees of New Graph Families Created from the Star Graph and the Examination of Their Entropies

Axioms
Complexity (number of spanning trees) is an essential and significant component in the design of communication networks (graphs). To ensure strong resistance and stiffness and to enhance the probability of a connection between two vertices, improvements ...
Salama Nagy Daoud, Ahmad Asiri
doaj   +1 more source