Distance (signless) Laplacian spectra and energies of two classes of cyclic polyomino chains

Yonghong Zhang and Ligong Wang

Applied Mathematics and Computation, 2025, vol. 487, issue C

Abstract: Let D(G) and Tr(G) be the distance matrix and the diagonal matrix of vertex transmissions of a graph G, respectively. The distance Laplacian matrix and the distance signless Laplacian matrix of G are defined as DL(G)=Tr(G)−D(G) and DQ(G)=Tr(G)+D(G), respectively. In this paper, we consider the distance Laplacian spectra and the distance signless Laplacian spectra of the linear cyclic polyomino chain Fn and the Möbius cyclic polyomino chain Mn. By utilizing the properties of circulant matrices, we give the characteristic polynomials and the eigenvalues for the distance Laplacian matrices and the distance signless Laplacian matrices of the graphs Fn and Mn, respectively. Furthermore, we provide the exactly values of the distance Laplacian energy and the distance signless Laplacian energy of the graph Fn, and the upper bounds on the distance Laplacian energy and the distance signless Laplacian energy of the graph Mn, respectively.

Keywords: Characteristic polynomial; Polyomino chain; Circulant matrix; Distance Laplacian matrix; Spectrum; Energy (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:487:y:2025:i:c:s0096300324005605

DOI: 10.1016/j.amc.2024.129099

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