On the spectrum of the normalized Laplacian of iterated triangulations of graphs

TL;DR

This paper analyzes the eigenvalues of the normalized Laplacian in iterated triangulations of graphs, revealing insights into their structure and related dynamical properties, with explicit formulas for key graph invariants.

Contribution

It provides explicit spectral characterizations and formulas for invariants of iterated triangulations of graphs, extending understanding of their structural and dynamical features.

Findings

Spectra of normalized Laplacian for iterated triangulations are explicitly determined.

Closed-form expressions for degree-Kirchhoff index, Kemeny's constant, and spanning trees are derived.

Results connect spectral properties with topological and dynamical graph characteristics.

Abstract

The eigenvalues of the normalized Laplacian of a graph provide information on its topological and structural characteristics and also on some relevant dynamical aspects, specifically in relation to random walks. In this paper we determine the spectra of the normalized Laplacian of iterated triangulations of a generic simple connected graph. As an application, we also find closed-forms for their multiplicative degree-Kirchhoff index, Kemeny's constant and number of spanning trees.