Abstract: | Let G be a k-connected graph of order n. For an independent set c, let d(S) be the number of vertices adjacent to at least one vertex of S and > let i(S) be the number of vertices adjacent to at least |S| vertices of S. We prove that if there exists some s, 1 ≤ s ≤ k, such that ΣxiEX d(X\{Xi}) > s(n?1) – ks/2] – i(X)(s?1)/2] holds for every independetn set X ={x0, x1 ?xs} of s + 1 vertices, then G is hamiltonian. Several known results, including Fraisse's sufficient condition for hamiltonian graphs, are dervied as corollaries. |