Journal ArticleDOI
Applications of laplacian spectra on a 3-prism graph
TLDR
In this article, the Laplacian spectra of a 3-prism graph with planar and polyhedral structure were calculated and applied to calculate the number of spanning trees and mean first-passage time.Abstract:
In this paper, we calculate the Laplacian spectra of a 3-prism graph and apply them. This graph is both planar and polyhedral, and belongs to the generalized Petersen graph. Using the regular structures of this graph, we obtain the recurrent relationships for Laplacian matrix between this graph and its initial state — a triangle — and further derive the corresponding relationships for Laplacian eigenvalues between them. By these relationships, we obtain the analytical expressions for the product and the sum of the reciprocals of all nonzero Laplacian eigenvalues. Finally we apply these expressions to calculate the number of spanning trees and mean first-passage time (MFPT) and see that the scaling of MFPT with the network size N is N2, which is larger than those performed on some uniformly recursive trees.read more
Citations
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Journal ArticleDOI
Applications of Laplacian spectra for n-prism networks
TL;DR: The analytical expressions for the product and the sum of reciprocals of all nonzero Laplacian eigenvalues are derived and used to handle various problems that often arise in the study of networks including Kirchhoff index, global mean-first passage time, average path length and the number of spanning trees.
Journal ArticleDOI
Counting spanning trees in prism and anti-prism graphs
TL;DR: This paper calculates the number of spanning trees in prism and antiprism graphs corresponding to the skeleton of a prism and an antiprisms by the electrically equivalent transformations and rules of weighted generating function and derives the analytical expressions for enumeration of spanning Trees.
Journal ArticleDOI
Coherence in a family of tree networks with an application of Laplacian spectrum
TL;DR: It is seen that the scalings of first and second order coherence with network size N are lnN and N, which are smaller than some studied tree graphs, such as Peano basin fractal, T-graph, and generalized Vicsek fractal.
Journal ArticleDOI
Network coherence in the web graphs
TL;DR: The scalings of network coherence in web graphs with a special feature that its fractal dimension is infinite are obtained and it is shown that the scalings are not related to the fractaldimension of web graphs.
Journal ArticleDOI
Laplacian spectrum of a family of recursive trees and its applications in network coherence
TL;DR: In this article, a family of uniform recursive trees is chosen as a model for network coherence, and a method to calculate the first-and second-order coherence is proposed.
References
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Evolutionary games on graphs
György Szabó,Gábor Fáth +1 more
TL;DR: The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.