A sharp lower bound on the signless Laplacian index of graphs with (κ,τ)-regular sets

Abstract

A new lower bound on the largest eigenvalue of the signless Laplacian spectra for graphs with at least one (κ,τ)regular set is introduced and applied to the recognition of non-Hamiltonian graphs or graphs without a perfect matching. Furthermore, computational experiments revealed that the introduced lower bound is better than the known ones. The paper also gives sufficient condition for a graph to be non Hamiltonian (or without a perfect matching).

Keywords

• graph spectra
• signless laplacian index
• hamiltonian graphs
• perfect matching
• 15a18
• 05c45
• 05c50
• 05c70