Summary
Graph theory provides a technique for disabling redundant links of a network in order to avoid the switching loop problem. In this paper, we investigate the use of the duality algebraic criteria to find the spanning trees of some switched planar networks. Based on recursive functions, we give new methods that enumerate the spanning trees of some dual graphs. Our theoretical approach guaranties both simplicity and efficiency when compared with the existing approaches and considering the grid network as an application.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Lotfi, D., El Marraki, M., Modabish, A.: Recursive relation for counting the complexity of butterfly map. Journal of Theoretical and Applied Information Technology 21(1), 43–46 (2011)
Lotfi, D., El Marraki, M., Aboutajdine, D.: Spanning tree recursions for crosses maps. Journal of Theoretical and Applied Information Technology 31(1), 1–7 (2011)
Myers, B.R.: Number of spanning trees in a wheel. IEEE Transactions on Circuit Theory CT-18, 280–282 (1971)
Modabish, A., Lotfi, D., El Marraki, M.: The number of spanning trees of planar maps: theory and applications. In: Proceeding of the International Conference on Multimedia Computing and Systems IEEE, ICMCS 2011, Ouarzazate, Morocco, pp. 1–6 (2011)
Modabish, A., El Marraki, M.: The number of spanning trees of certain families of planar maps. Applied Mathematical Sciences 5(18), 883–898 (2011)
Haghighi, M.H.S., Bibak, K.: Recursive relations for the number of spanning trees. Applied Mathematical Sciences 3(46), 2263–2269 (2009)
Bogdanowicz, Z.R.: Formulas for the number of spanning trees in a fan. Applied Mathematical Sciences 2(16), 781–786 (2008)
Nishizeki, T., Saidur, R.M.: Planar Graph Drawing. Lecture Note Series on Computing, vol. 12. World Scientific Publishing Co. Pte. Ltd, Singapore (2004)
Desjarlais, M., Molina, R.: Counting spanning trees in grid graphs. Congressus Numerantium 145, 177–185 (2000)
Kirchhoff, G.: Über die auflösung der gleichungen auf. Welche man bei der Untersuchung der Linearen Verteilung Galvanischer Ströme geführt Wird. Ann. Phy. Chem. 72, 497–508 (1847)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lotfi, D., El Marraki, M., Aboutajdine, D. (2013). Spanning Trees Structures of Communications Networks. In: Choraś, R. (eds) Image Processing and Communications Challenges 4. Advances in Intelligent Systems and Computing, vol 184. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32384-3_34
Download citation
DOI: https://doi.org/10.1007/978-3-642-32384-3_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32383-6
Online ISBN: 978-3-642-32384-3
eBook Packages: EngineeringEngineering (R0)