Аннотация:
For a graph $ G$, a set $ S\subseteq V(G) $ is a disjunctive total dominating set if every vertex has a neighbor in $ S $ or has at least two vertices in $ S $ at distance two from it. The disjunctive total domination number of $ G $ is the minimum cardinality of such a set. In this paper, we study disjunctive total domination on the corona and join of graphs. We give some results and establish an upper bound for disjunctive total domination of corona of two graphs. Moreover, we determine the disjunctive total domination number of corona $ G\circ H$, in which $ G $ is a star, cycle, complete graph, wheel graph or complete bipartite graph and $ H $ is any graph. On the other hand, we determine the disjunctive total domination number of subdivision-vertex and subdivision-edge join of any two graphs.
