The normalized Laplacian spectrum of quadrilateral graphs and its applications

Deqiong Li and Yaoping Hou

Applied Mathematics and Computation, 2017, vol. 297, issue C, 180-188

Abstract: The quadrilateral graph Q(G) of G is obtained from G by replacing each edge in G with two parallel paths of lengths 1 and 3. In this paper, we completely describe the normalized Laplacian spectrum on Q(G) for any graph G. As applications, the significant formulae to calculate the multiplicative degree-Kirchhoff index, the Kemeny’s constant and the number of spanning trees of Q(G) and the quadrilateral iterative graph Qr(G) are derived.

Keywords: Quadrilateral; Normalized Laplacian spectrum; Multiplicative degree-Kirchhoff index; Kemeny’s constant; The number of spanning trees (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:297:y:2017:i:c:p:180-188

DOI: 10.1016/j.amc.2016.10.041

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