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

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 641-648
- ISSN: 2391-5455

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topYilun Shang. "On the number of spanning trees, the Laplacian eigenvalues, and the Laplacian Estrada index of subdivided-line graphs." Open Mathematics 14.1 (2016): 641-648. <http://eudml.org/doc/286753>.

@article{YilunShang2016,

abstract = {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).},

author = {Yilun Shang},

journal = {Open Mathematics},

keywords = {Laplacian Estrada index; Subdivide-line graph; Line graph; Laplacian spectrum; Spanning tree; Laplacian estrada index; subdivide-line graph; line graph; spanning tree},

language = {eng},

number = {1},

pages = {641-648},

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

url = {http://eudml.org/doc/286753},

volume = {14},

year = {2016},

}

TY - JOUR

AU - Yilun Shang

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

JO - Open Mathematics

PY - 2016

VL - 14

IS - 1

SP - 641

EP - 648

AB - 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).

LA - eng

KW - Laplacian Estrada index; Subdivide-line graph; Line graph; Laplacian spectrum; Spanning tree; Laplacian estrada index; subdivide-line graph; line graph; spanning tree

UR - http://eudml.org/doc/286753

ER -

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