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

• Autorzy: Yilun Shang
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

Laplacian Estrada index; Subdivide-line graph; Line graph; Laplacian spectrum; Spanning tree

Kategorie tematyczne

• 05C30: Enumeration in graph theory
• 05C05: Trees
• 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
• 05C76: Graph operations (line graphs, products, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 641-648

Daty

wydano

2016-01-01

otrzymano

2016-05-27

zaakceptowano

2016-08-09

online

2016-09-15

Twórcy

autor

Yilun Shang

• School of Mathematical Sciences, Tongji University, Shanghai 200092,

Identyfikatory

DOI

10.1515/math-2016-0055