The paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram, S.M. Sheikholeslami, O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009), 622–628], we constructively characterize all connected unicyclic graphs with...

Let G = (V,E) be a graph without an isolated vertex. A set D ⊆ V (G) is a total dominating set if D is dominating and the in- duced subgraph G[D] does not contain an isolated vertex. The total domination number of G is the minimum cardinality of a total domi- nating set of G. A set D ⊆ V (G) is a total outer–connected dominating set if D is total dominating and the induced subgraph G[V (G)−D] is a connected graph. The total outer–connected...

A simple, efficient two-step method for the preparation of heterobicyclic compounds was developed. Starting from 5-acyl or 5-carbamoyl-2,2- dimethyl-1,3-dioxa-4,5-dione bicyclic scaffolds of 1-azabicyclo[5.2.0]non- 3-en-9-one, 6,9,10,10a-tetrahydro-4H-[1,3]oxazino[3,2-a]azepin-4-one, and 6,9,10,10a-tetrahydro-2H-[1,3]oxazino[3,2-a]azepine-2,4(3H)-dione were prepared using cycloaddition of thermally generated ketenes to aldimines...