In this paper, k + 1 real numbers c1, c2, ?, ck+1 are found such that the following condition is sufficient for a k-connected graph of order n to be hamiltonian: for each independent vertex set of k + 1 vertices in G. where Si = {v ? V:|N(v) ∩ S| = i} for 0 ≦ i ≦ k + 1. Such a set of k + 1 numbers is called an Hk-sequence. A sufficient condition for the existence of Hk-sequences is obtained that generalizes many known results involving sum of degrees, neighborhood unions, and/or neighborhood intersections.
