On (<i>t, r</i>) Broadcast Domination of Directed Graphs

A dominating set of a graph G is vertices that contains at least one endpoint every edge on the graph. The domination number order minimum G. (t, r) broadcast generalization in which broadcasting emits signals strength t decrease by 1 as they traverse each edge, and we require vertex receives cumulative signal r from its neighbors. In this paper, extend study to directed graphs. Our main result explores interval values obtained considering numbers all orientations particular, prove cases = (2, 2), for integer value interval, there exists an orientation has equal value. We also investigate finite grid graph, star infinite triangular lattice conclude with some directions future study.