Spectral Radius and Hamiltonicity of graphs

TL;DR

This paper explores how spectral properties of graphs, such as spectral radius and signless Laplacian spectral radius, relate to Hamiltonicity and traceability in various classes of graphs, providing new spectral conditions for these properties.

Contribution

It introduces novel spectral conditions for Hamilton-connectedness and traceability in graphs and bipartite graphs, extending previous combinatorial criteria.

Findings

Spectral radius conditions for Hamilton-connectedness.

Spectral radius criteria for traceability in bipartite graphs.

New spectral bounds related to graph Hamiltonicity.

Abstract

In this paper, we study the Hamiltonicity of graphs with large minimum degree. Firstly, we present some conditions for a simple graph to be Hamilton-connected and traceable from every vertex in terms of the spectral radius of the graph or its complement respectively. Secondly, we give the conditions for a nearly balanced bipartite graph to be traceable in terms of spectral radius, signless Laplacian spectral radius of the graph or its quasi-complement respectively.