NDLI: Counting the number of spanning trees of generalization Farey graph

Content Provider	IEEE Xplore Digital Library
Author	Yuzhi Xiao Haixing Zhao
Copyright Year	2013
Description	Author affiliation: Sch. of Comput. Sci., ShaanXi Normal Univ., Xi'an, China (Yuzhi Xiao) \|\| Sch. of Comput., Qinghai Normal Univ., Xining, China (Haixing Zhao)
Abstract	Spanning trees are an important quantity characterizing the reliability of a network, however, explicitly determining the number of spanning trees in networks is a theoretical challenge. In this paper, we perform a study on the enumeration of spanning trees in a specific small-world network with an exponential distribution of vertex degrees, which is called generalization Farey graph since it is associated with the famous Farey sequence. According to the particular network structure, use the method, proposed by us, we obtain the exact number of spanning trees in the Farey graph. The result shows that the computation complexity is O(n), which is better than that of the matrix tree theorem with $O(n^{2}),$ where n is the number of steps. We derive a basic property of generalization Farey graph controlled by a parameter k, which is closely to the number of spanning trees of network, which become bigger with increasing k. We also obtain the maximum and minimum numbers of spanning trees of these kinds of networks through the method.
Sponsorship	IEEE Circuits Syst. Soc.
Starting Page	1778
Ending Page	1782
File Size	245663
Page Count	5
File Format	PDF
ISBN	9781467347143
ISSN	21579563
DOI	10.1109/ICNC.2013.6818271
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-07-23
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Lattices Vegetation Reliability theory Educational institutions Entropy Complexity theory
Content Type	Text
Resource Type	Article

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