"The (t,r) Broadcast Domination Number of Directed Graphs"

"(t,r) broadcast domination is a generalization of standard graph domination defined using the following analogy. Consider a set of cell phone towers in a graph, each with a known signal strength t. Each tower gives itself signal strength t, each neighbor of this tower receives signal strength t-1, each neighbor’s neighbor receives signal strength t-2, and so on, until the signal dies out (i.e., reaches strength 0). If there are multiple towers whose signal reaches a single cell phone, those signal strengths add together. Given an integer r, the (t,r) broadcast domination number is the minimal number of towers of signal strength needed to ensure that every cell phone on this graph has signal strength at least r. In this thesis, we define the directed (t,r) broadcast domination number of a graph and present results related to this new graph parameter."

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