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

This paper mainly focuses on spectral conditions for the Hamiltonicrty of balanced bipartite graphs and nearly balanced bipartite graphs Let p(G) and q(G) 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 order2n and of min u degree S(G) > k > s > 0 (1) If n k 1){k 1 and p G P t/k'k-5 then G is 2shamiltonian unless G = 8ri7771k`k-5 (ii) n (k+ 1){k s + 1) and q{G} (if 13,?,,-k then G is 2 hamiltonian unless G = EC-1ick-s This theorem generalizes the results in [B.L.Li, B. Ning, Spectral analogues of Erdos' and Moon -Maser's th7o2 r25ms on