(t,r) Broadcast domination number of the join and corona of graphs

Abstract

Let G be a graph and u, v ∈ V ( G ). If t ∈ N , then the reception strength of u with respect to t and v is given by r tv ( u ) = t − d ( u, v ) if t ≥ d ( u, v ) and r tv ( u ) = 0 if t < d ( u, v ). If S ⊆ V ( G ), then the reception strength of u with respect to t and S is given by P v ∈ S r tv ( u ). We say that S is a ( t, r ) broadcast dominating set in G if the reception strength of u with respect to t and S is greater than or equal r for all vertices u . The ( t, r ) broadcast domination number of G is the minimum cardinality of a ( t, r ) broadcast dominating set of G . In this paper, we gave the ( t, r ) broadcast domination number of paths, cycles, complete graphs, the join of two arbitrary graphs, and the corona of two arbitrary graphs.