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On the number of spanning trees, the Laplacian eigenvalues, and the Laplacian Estrada index of subdivided-line graphs

100%

Shang Y.

Open Mathematics

2016

tom 14

nr 1

641-648

As a generalization of the Sierpiński-like graphs, the subdivided-line graph Г(G) of a simple connected graph G is defined to be the line graph of the barycentric subdivision of G. In this paper we obtain a closed-form formula for the enumeration of spanning trees in Г(G), employing the theory of electrical networks. We present bounds for the largest and second smallest Laplacian eigenvalues of Г(G) in terms of the maximum degree, the number of edges, and the first Zagreb index of G. In addition, we establish upper and lower bounds for the Laplacian Estrada index of Г(G) based on the vertex degrees of G. These bounds are also connected with the number of spanning trees in Г(G).

Lack of Gromov-hyperbolicity in small-world networks

100%

Shang Y.

Open Mathematics

2012

tom 10

nr 3

1152-1158

The geometry of complex networks is closely related with their structure and function. In this paper, we investigate the Gromov-hyperbolicity of the Newman-Watts model of small-world networks. It is known that asymptotic Erdős-Rényi random graphs are not hyperbolic. We show that the Newman-Watts ones built on top of them by adding lattice-induced clustering are not hyperbolic as the network size goes to infinity. Numerical simulations are provided to illustrate the effects of various parameters on hyperbolicity in this model.

Ograniczanie wyników

2 Open Mathematics

2 Shang Y.

1 2016

1 2012

Wyniki wyszukiwania

On the number of spanning trees, the Laplacian eigenvalues, and the Laplacian Estrada index of subdivided-line graphs

Lack of Gromov-hyperbolicity in small-world networks