Abstract
1 Introduction In this note we consider simple graphs only, following Bondy and Murty for basic graph-theoretic notations and terminology. In addition, we set G_n~k={G|G is a k-connected graph of order n}, H_c={G|G is a Hamiltonian connected graph}, and denote by P_H(u,v)a Hamiltonian u-v path. A path P in a graph G is called a dominating path if every edge of G has at least one of its end vertices on P. α and K denote the independence number and connectivity of G.
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