Spectral conditions of complement for some graphical properties

TL;DR

This paper establishes spectral radius-based conditions on the complement of a graph with large minimum degree to ensure various connectivity and Hamiltonian properties, extending previous spectral graph theory results.

Contribution

It provides new spectral radius criteria for multiple graph properties related to connectivity and Hamiltonicity, focusing on the complement of the graph.

Findings

Spectral radius conditions for s-connectedness

Spectral radius conditions for s-edge-connectedness

Spectral radius conditions for s-Hamiltonian and related properties

Abstract

L.H. Feng at el \cite{feng4} present sufficient conditions based on spectral radius for a graph with large minimum degree to be $s$-path-coverable and $s$-Hamiltonian. Motivated by this study, in this paper, we give the sufficient conditions for a graph with large minimum degree to be $s$-connected, $s$-edge-connected, $\beta$-deficient, $s$-path-coverable, $s$-Hamiltonian and $s$-edge-Hamiltonian in terms of spectral radius of its complement.