Spectral conditions for a graph to be Hamilton-connected

TL;DR

This paper establishes spectral criteria involving adjacency and signless Laplacian matrices that guarantee a graph is Hamilton-connected, and provides conditions for Hamiltonian paths and cycles based on spectral radius.

Contribution

It introduces new spectral conditions for Hamilton-connectedness and Hamiltonian paths using adjacency and signless Laplacian spectra, extending previous graph theory results.

Findings

Spectral conditions for Hamilton-connectedness based on spectral radius

Sufficient spectral conditions for Hamiltonian paths and cycles

Use of adjacency and signless Laplacian matrices in spectral graph theory

Abstract

In this paper we establish some spectral conditions for a graph to be Hamilton-connected in terms of the spectral radius of the adjacency matrix or the signless Laplacian of the graph or its complement. For the existence of Hamiltonian paths or cycles in a graph, we also give a sufficient condition by the signless Laplacian spectral radius.