Degree sum and connectivity conditions for dominating cycles Original Research Article

For a graph G, let image be the minimum degree sum of an independent set of k vertices. Ore showed that if G is a graph of order image with image then G is hamiltonian. Let image be the connectivity of a graph G. Bauer, Broersma, Li and Veldman proved that if G is a 2-connected graph on n vertices with image, then G is hamiltonian. On the other hand, Bondy showed that if G is a 2-connected graph on n vertices with image, then each longest cycle of G is a dominating cycle. In this paper, we prove that if G is a 3-connected graph on n vertices with image, then G contains a longest cycle which is a dominating cycle.