Counting spanning trees in a small-world Farey graph

Details Counting spanning trees in a small-world Farey graph Counting spanning trees in a small-world Farey graph

2012-01-20

arxiv.org/abs/1201.4228v1

Physica A 391 (2012) 3342-3349

Physics

Condensed Matter

Statistical Mechanics

Definitive version accepted for publication in Physica A

Scientific paper

10.1016/j.physa.2012.01.039

The problem of spanning trees is closely related to various interesting problems in the area of statistical physics, but determining the number of spanning trees in general networks is computationally intractable. 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 a Farey graph since it is associated with the famous Farey sequence. According to the particular network structure, we provide some recursive relations governing the Laplacian characteristic polynomials of a Farey graph and its subgraphs. Then, making use of these relations obtained here, we derive the exact number of spanning trees in the Farey graph, as well as an approximate numerical solution for the asymptotic growth constant characterizing the network. Finally, we compare our results with those of different types of networks previously investigated.

Affiliated with

Also associated with

No associations

Rating

Counting spanning trees in a small-world Farey graph does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Counting spanning trees in a small-world Farey graph, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Counting spanning trees in a small-world Farey graph will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-320482