Spectral analogues of Moon-Moser's theorem on Hamilton paths in bipartite graphs

In 1962, Erd\H{o}s proved a theorem on the existence of Hamilton cycles in graphs under minimum degree and edge number condition. Significantly strengthening in case of a balanced bipartite graph, Moon and Moser proved a corresponding theorem in 1963. In this paper we establish several spectral analogues of Moon and Moser's theorem on Hamilton paths in balanced bipartite graphs and nearly balanced bipartite graphs.