A set C of vertices in a graph G = (V,E) is total dominating in G if all vertices of V are adjacent to a vertex of C. Furthermore, if a total dominating set C in G has the additional property that for any distinct vertices u, v ∈ V \ C the subsets formed by the vertices of C respectively adjacent to u and v are different, then we say that C is a locating-total dominating set in G. Previously, l...

In a consecutive series of 100 cases of Fallot's tetralogy undergoing total correction, the mean birthweight was found to be just below the 50th centile. Blalock-Taussig or Waterston shunts were performed in 45 patients. Before their shunt operations a significant number of patients had become retarded in height and weight development but after the shunt operations many patients showed accelera...

The height (as in [3] and [4]) of a point in a rooted tree is the length of the path (that is, the number of lines in the path) from it to the root; the total height of a rooted tree is the sum of the heights of its points. The latter arises naturally in studies of random neural networks made by one of us (N.J.A.S.), where the enumeration of greatest interest is that of trees with all points di...