Hamiltonian graphs with neighborhood intersections

In this paper, k + 1 real numbers c 1 , c 2 , ⃛, c k +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 S i = {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.