The Laplacian Eigenvalues and Invariants of Graphs

TL;DR

This paper explores the relationship between Laplacian eigenvalues and various graph invariants, providing conditions for Hamiltonicity based on spectral properties.

Contribution

It introduces new links between Laplacian eigenvalues and graph invariants, including a sufficient condition for Hamiltonian cycles.

Findings

Established relations between Laplacian eigenvalues and graph connectivity

Provided a spectral condition for Hamiltonicity

Linked Laplacian spectra to forwarding indices

Abstract

In this paper, we investigate some relations between the invariants (including vertex and edge connectivity and forwarding indices) of a graph and its Laplacian eigenvalues. In addition, we present a sufficient condition for the existence of Hamiltonicity in a graph involving its Laplacian eigenvalues.