Signless Laplacian spectral radius and Hamiltonicity of graphs with large minimum degree

TL;DR

This paper provides new spectral conditions based on the signless Laplacian spectral radius that guarantee Hamiltonicity in graphs with large minimum degree, including bipartite graphs, and introduces extremal graph characterizations.

Contribution

It establishes tight spectral conditions for Hamiltonicity related to the signless Laplacian spectral radius and characterizes extremal graphs, extending to bipartite graphs.

Findings

Derived tight spectral conditions for Hamiltonicity.

Characterized extremal graphs achieving these bounds.

Constructed infinite examples demonstrating the strength of the results.

Abstract

In this paper, we establish a tight sufficient condition for the Hamiltonicity of graphs with large minimum degree in terms of the signless Laplacian spectral radius and characterize all extremal graphs. Moreover, we prove a similar result for balanced bipartite graphs. Additionally, we construct infinitely many graphs to show that results proved in this paper give new strength for one to determine the Hamiltonicity of graphs.