Existence of spanning and dominating trails and circuits

Let T be a trail of a graph G. T is a spanning trail (S-trail) if T contains all vertices of G. T is a dominating trail (D-trail) if every edge of G is incident with at least one vertex of T. A circuit is a nontrivial closed trail. Sufficient conditions involving lower bounds on the degree-sum of vertices or edges are derived for graphs to have an S-trail, S-circuit, D-trail, or D-circuit. Thereby a result of Brualdi and Shanny and one mentioned by Lesniak-Foster and Williamson are improved.