Abstract
The objective of this paper is to propose an algorithm to generate all possible structures of spanning trees of an undirected complete graph of n vertices. The process starts with a star-tree (T) of the given complete graph and then replacing the edges of T one by one to generate different possible structures like chain, branch, etc. These spanning tree structures repeat themselves as we move from lower to higher values of n. The authors have attempted to find out some generalized expressions for different structures of spanning trees for a complete graph of order n.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M. Chakraborty, S. Chowdhury, R.K. Pal, Two algorithms for computing all spanning trees of a simple, undirected, and connected graph: once assuming a complete graph. IEEE Access 6, 56290–56300 (2018)
M. Chakraborty, R. Mehera, R.K. Pal, A divide-and-conquer algorithm for all spanning tree generation, in Proceedings of the 3rd International Doctoral Symposium on Applied Computation and Security Systems (ACSS), Proceedings Published as Book Chapter of the Series Advances in Intelligent Systems and Computing, vol. 567 (Springer, 2016), pp. 19–36
J.P. Char, Generation of trees, two-trees and storage of master forests. IEEE Trans. Circuit Theory CT-15, 128–138 (1968)
S.L. Hakimi, On trees of a graph and their generation. J. Franklin Inst. 272(5), 347–359 (1961)
S. Kapoor, H. Ramesh, Algorithms for enumerating all spanning trees of undirected and weighted graphs. SIAM J. Comput. 24(2), 247–265 (1995)
G.J. Minty, A simple algorithm for listing all the trees of a graph. IEEE Trans. Circuit Theory CT-12, 120 (1965)
S. Naskar, K. Basuli, S. Sen Sarma, Generation of all spanning trees. Soc. Sci. Res. Netw. (2009)
S. Sen Sarma, A. Rakshit, R.K. Sen, A.K. Choudhury, An efficient tree generation algorithm. IETE J. Res. 27(3), 105–109 (1981)
Wikipedia, Cayley’s formula. https://en.wikipedia.org/wiki/Cayley%27s_formula
P. Winter, An algorithm for the enumeration of spanning trees. BIT Numer. Math. 26(1), 44–62 (1986)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Datta, S., Chakraborty, S., Chakraborty, M., Pal, R.K. (2021). Algorithm to Generate All Spanning Tree Structures of a Complete Graph. In: Balas, V.E., Hassanien, A.E., Chakrabarti, S., Mandal, L. (eds) Proceedings of International Conference on Computational Intelligence, Data Science and Cloud Computing. Lecture Notes on Data Engineering and Communications Technologies, vol 62. Springer, Singapore. https://doi.org/10.1007/978-981-33-4968-1_14
Download citation
DOI: https://doi.org/10.1007/978-981-33-4968-1_14
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-33-4967-4
Online ISBN: 978-981-33-4968-1
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)