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2018 The Evaluation of the Number and the Entropy of Spanning Trees on Generalized Small-World Networks
Raihana Mokhlissi, Dounia Lotfi, Joyati Debnath, Mohamed El Marraki, Noussaima EL Khattabi
J. Appl. Math. 2018: 1-7 (2018). DOI: 10.1155/2018/1017308

Abstract

Spanning trees have been widely investigated in many aspects of mathematics: theoretical computer science, combinatorics, so on. An important issue is to compute the number of these spanning trees. This number remains a challenge, particularly for large and complex networks. As a model of complex networks, we study two families of generalized small-world networks, namely, the Small-World Exponential and the Koch networks, by changing the size and the dimension of the cyclic subgraphs. We introduce their construction and their structural properties which are built in an iterative way. We propose a decomposition method for counting their number of spanning trees and we obtain the exact formulas, which are then verified by numerical simulations. From this number, we find their spanning tree entropy, which is lower than that of the other networks having the same average degree. This entropy allows quantifying the robustness of the networks and characterizing their structures.

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Raihana Mokhlissi. Dounia Lotfi. Joyati Debnath. Mohamed El Marraki. Noussaima EL Khattabi. "The Evaluation of the Number and the Entropy of Spanning Trees on Generalized Small-World Networks." J. Appl. Math. 2018 1 - 7, 2018. https://doi.org/10.1155/2018/1017308

Information

Received: 19 April 2018; Accepted: 8 July 2018; Published: 2018
First available in Project Euclid: 10 October 2018

zbMATH: 07051352
MathSciNet: MR3854938
Digital Object Identifier: 10.1155/2018/1017308

Rights: Copyright © 2018 Hindawi

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