The Laplacian and normalized Laplacian spectra of Mobius polyomino networks and their applications

TL;DR

This paper analyzes the spectral properties of Mobius polyomino networks and derives various network invariants, revealing a surprising relationship between the Kirchhoff and multiplicative degree-Kirchhoff indices.

Contribution

It provides the first spectral analysis of Mobius polyomino networks and computes key network invariants using spectral theory.

Findings

Kirchhoff index and related invariants are explicitly calculated.

The multiplicative degree-Kirchhoff index is nine times the Kirchhoff index.

Spectral properties reveal structural insights of Mobius polyomino networks.

Abstract

Spectral theory has widely used in complex networks and solved some practical problems. In this paper, we investigated the Laplacian and normalized Laplacian spectra of Mobius polyomino networks by using spectral theory. Let Mn denote Mobius polyomino networks (n>=3). As applications of the obtained results, the Kirchhoff index, multiplicative degree-Kirchhoff index, Kemeny's constant and spanning trees of Mn are obtained. Moreover, it is surprising to find that the multiplicative degree-Kirchhoff index of Mn is nine times as much as the Kirchhoff index.