Abstract
Let T1, T2 be spanning trees in a graph G. If for any two vertices u, v of G, the paths from u to v in T1, T2 are vertex-disjoint except end vertices u and v, then T1, T2 are called two completely independent spanning trees (CISTs for short) in Pai and Chang [12] proposed an approach to recursively construct two CISTs in several hypercube-variant networks, including crossed cubes. For every kind of n-dimensional variant cube, the diameters of two CISTs for their construction are 2n − 1. In this paper, we give a new algorithm to construct two CISTs T1 and T2 in n-dimensional crossed cubes, and show that diam(T1) = diam(T2) = 2n − 2 if n ∈ {4,5}; and diam(T1) = diam(T2) = 2n − 3 if n ≥ 6 where diam(G) is the diameter of graph G.
Keywords
- Interconnection networks
- Completely independent spanning trees
- Crossed cubes
- Diameter
This is a preview of subscription content, access via your institution.
Buying options
References
Araki, T.: Dirac’s condition for completely independent spanning trees. J. Graph Theory 77, 171–179 (2014)
Chang, H.Y., Wang, H.L., Yang, J.S., Chang, J.M.: A note on the degree condition of completely independent spanning trees. IEICE Trans. Fundam. E98-A, 2191–2193 (2015)
Darties, B., Gastineau, N., Togni, O.: Completely independent spanning trees in some regular graphs. Discrete Appl. Math. 217, 163–174 (2017)
Efe, K.: The crossed cube architecture for parallel computation. IEEE Trans. Parallel Distrib. Syst. 3, 513–524 (1992)
Fan, G., Hong, Y., Liu, Q.: Ore’s condition for completely independent spanning trees. Discrete Appl. Math. 177, 95–100 (2014)
Hasunuma, T.: Completely independent spanning trees in the underlying graph of a line digraph. Discrete Math. 234, 149–157 (2001)
Hasunuma, T.: Completely independent spanning trees in maximal planar graphs. In: Goos, G., Hartmanis, J., van Leeuwen, J., Kučera, L. (eds.) WG 2002. LNCS, vol. 2573, pp. 235–245. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-36379-3_21
Hasunuma, T.: Minimum degree conditions and optimal graphs for completely independent spanning trees. In: Lipták, Z., Smyth, W.F. (eds.) IWOCA 2015. LNCS, vol. 9538, pp. 260–273. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-29516-9_22
Hasunuma, T., Morisaka, C.: Completely independent spanning trees in torus networks. Networks 60, 59–69 (2012)
Hong, X., Liu, Q.: Degree condition for completely independent spanning trees. Inform. Process. Lett. 116, 644–648 (2016)
Matsushita, M., Otachi, Y., Araki, T.: Completely independent spanning trees in (partial) k-trees. Discuss. Math. Graph Theory 35, 427–437 (2015)
Pai, K.J., Chang, J.M.: Constructing two completely independent spanning trees in hypercube-variant networks. Theor. Comput. Sci. 652, 28–37 (2016)
Pai, K.J., Chang, J.M.: Improving the diameters of completely independent spanning trees in locally twisted cubes. Inform. Process. Lett. 141, 22–24 (2019)
Acknowledgments
This research was partially supported by MOST grants 107-2221-E-131-011 from the Ministry of Science and Technology, Taiwan.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Pai, KJ. (2019). Designing an Algorithm to Improve the Diameters of Completely Independent Spanning Trees in Crossed Cubes. In: Chang, CY., Lin, CC., Lin, HH. (eds) New Trends in Computer Technologies and Applications. ICS 2018. Communications in Computer and Information Science, vol 1013. Springer, Singapore. https://doi.org/10.1007/978-981-13-9190-3_46
Download citation
DOI: https://doi.org/10.1007/978-981-13-9190-3_46
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-9189-7
Online ISBN: 978-981-13-9190-3
eBook Packages: Computer ScienceComputer Science (R0)