Bounds on Signless Laplacian Eigenvalues of Hamiltonian Graphs

Abstract

We give an upper bound on the largest eigenvalue of the signless Laplacian matrix of a Hamiltonian graph. This bound is applied to obtain sufficient spectral conditions for the non-existence of Hamiltonian cycles. Under certain additional assumptions we provide a polynomial time decisive spectral criterion for the Hamiltonicity of a given graph with sufficiently large minimum vertex degree.