Unified spectral hamiltonian results of balanced bipartite graphs and complementary graphs

TL;DR

This paper develops a unified spectral approach using the Bondy-Chvátal closure to establish sufficient eigenvalue conditions for Hamiltonian and path-coverable properties in balanced bipartite and complementary graphs, improving previous results.

Contribution

It introduces a unified spectral framework leveraging the Bondy-Chvátal closure to sharpen existing eigenvalue-based conditions for Hamiltonian properties in specific graph classes.

Findings

Provides new spectral conditions for Hamiltonian properties

Sharpens previous eigenvalue bounds in the literature

Unifies approaches for bipartite and complementary graphs

Abstract

There have been researches on sufficient spectral conditions for Hamiltonian properties and path-coverable properties of graphs. Utilizing the Bondy-Chv\'atal closure, we provide a unified approach to study sufficient graph eigenvalue conditions for these properties and sharpen former spectral results in [{\em Linear Algebra Appl.}, 432 (2010), 566-570], [{\em Linear Algebra Appl.}, 432 (2010), 2170-2173], [{\em Appl. Mech. Mater.}, 336-338 (2013), 2329-2334], [{\em Linear Algebra Appl.}, 467 (2015), 254-266], [{\em Linear Multilinear Algebra}, 64 (2016), 2252-2269], and [{\em J. Comb. Optim.}, 35 (2018), 1104-1127], among others.