Distance signless Laplacian spectral radius and Hamiltonian properties of graphs

TL;DR

This paper explores how the distance signless Laplacian spectral radius influences Hamiltonian properties of graphs, providing new spectral conditions for Hamilton-connectedness, traceability, and Hamiltonicity.

Contribution

It introduces novel spectral conditions based on the distance signless Laplacian for determining Hamiltonian properties in graphs.

Findings

A sufficient condition for bipartite graphs to be Hamilton-connected.

Two spectral conditions for a graph to be Hamilton-connected and traceable.

A spectral condition for a graph to be Hamiltonian based on the complement graph.

Abstract

In this paper, first, we establish a sufficient condition for a bipartite graph to be Hamilton-connected. Furthermore, we also give two sufficient conditions on distance signless Laplacian spectral radius for a graph to be Hamilton-connected and traceable from every vertex, respectively. Last, we obtain a sufficient condition for a graph to be Hamiltonian in terms of the distance signless Laplacian spectral radius of $G^{C}$.