Spectral radius and Hamiltonicity of graphs

TL;DR

This paper explores how the spectral radius of a graph's adjacency matrix can determine the presence of Hamiltonian cycles in the graph and its complement, providing spectral conditions for Hamiltonicity.

Contribution

It establishes new spectral criteria based on the largest eigenvalue for guaranteeing Hamiltonicity in graphs and their complements.

Findings

Spectral conditions for Hamiltonicity derived from the largest eigenvalue.

Criteria applicable to both the graph and its complement.

Enhanced understanding of spectral graph theory related to Hamiltonian cycles.

Abstract

Let G be a graph of given order and mu(G) be the largest eigenvalue of its adjacency matrix. We give conditions on mu(G) that imply Hamiltonicity of G and of its complement.