Some generalizations of spectral conditions for 2s-hamiltonicity and 2s-traceability of bipartite graphs

Abstract

ABSTRACT This paper mainly focuses on spectral conditions for the Hamiltonicity of balanced bipartite graphs and nearly balanced bipartite graphs. Let and be the spectral radius and signless Laplacian spectral radius of a graph G, respectively. One of our main results is the following theorem: Let G be a balanced bipartite graph of order and of minimum degree . If and , then G is -hamiltonian unless . If and , then G is -hamiltonian unless . This theorem generalizes the results in [B. L. Li, B. Ning, Spectral analogues of Erdos' and Moon–Moser's theorems on Hamilton cycles, Linear and Multilinear Algebra, 64 (2016) 2252–2269].