DOMINATING BROADCASTS IN GRAPH THEORY

A distribution of weights on vertices of a graph G is called a dominating broadcast if every vertex is dominated by some vertex with positive weight. Broadcast domination in graphs is a variation of domination in which different integer weights are allowed on vertices and a vertex with weight k dominates its distance k neighbourhood. The domination number (G) is the minimum cardinality of a minimal dominating set. The upper domination number (G) is the maximum cardinality of a minimal dominating set.