Two Algorithms for Computing All Spanning Trees of a Simple, Undirected, and Connected Graph: Once Assuming a Complete Graph
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This paper proposes altogether different and new approaches for the computation of all possible spanning trees of a simple, undirected, and connected graph and proposes to have novelties and limitations of its own.Abstract:
In this paper, we have proposed altogether different and new approaches for the computation of all possible spanning trees of a simple, undirected, and connected graph. Our proposed algorithms have the capability to solve the major bottlenecks in this area, namely, generation of duplicate trees and circuit checking. In the first algorithm, the given graph has been converted to its corresponding weighted complete graph, which proposes to have novelties and limitations of its own. In addition, we have also proposed another related algorithm, and as a result, we have been able to come up with new ideas in this research domain of graph theory.read more
Citations
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Journal ArticleDOI
Divide-and-conquer based all spanning tree generation algorithm of a simple connected graph
TL;DR: In this paper , an algorithm based on a new technique, namely divide-and-conquer, has been proposed for all spanning tree generation of a simple connected graph, which is a well-approached problem in graph theory.
Book ChapterDOI
Algorithm to Generate All Spanning Tree Structures of a Complete Graph
TL;DR: In this article, the authors proposed an algorithm to generate all possible structures of spanning trees of an undirected complete graph of n vertices, where the process starts with a star-tree (T) of the given complete graph and then replaces the edges of T one by one to generate different possible structures like chain, branch, etc.
References
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On trees of a graph and their generation
TL;DR: Those properties of a set of trees that aid us in generating the trees of a given graph are presented and two different methods for generating trees for graphs whose nullities are small in comparison to their ranks.
Journal ArticleDOI
A Flexible Algorithm for Generating All the Spanning Trees in Undirected Graphs
TL;DR: An algorithm for generating all the spanning trees in undirected graphs that requires O (n+m+ τ n) time where the given graph has n vertices, m edges, and τ spanning trees.
Journal ArticleDOI
An algorithm for the enumeration of spanning trees
TL;DR: In this paper a new enumeration algorithm based on the idea of contractions of the graph is presented and computational analysis indicates that the algorithm requires less computation time than any other of the previously best-known algorithms.
Journal ArticleDOI
An Efficient Tree-Generation Algorithm
TL;DR: An algorithm for generation of trees of a connected, non-oriented, and simple graph is presented and the time complexity is drastically reduced compared to the brute-force technique.
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