On k-ordered Graphs Involved Degree Sum

Abstract A graph G is k-ordered Hamiltonian,2≤k≤n,if for every ordered sequence S of k distinctvertlces of G,there exists a Hamiltonian cycle that encounters S in the given order. In this article, we provethat if G is a graph on n vertices with degree sum of nonadjacent vertices at least n+3k-9/2,then G is k-orderedHamiltonian for k=3,4,…,[n/19].We also show that the degree sum bound can be reduced to n+2[k/2]-2 ifk(G)≥3k-1/2 or δ(G)≥5k-4.Several known results are generalized.