(t,r) Broadcast Domination on Directed Graphs by Peter Hollander ’21, Mathematics Senior Thesis Defense, Monday, April 26, 1 – 1:40 pm, live talk can be accessed at https://williams.zoom.us/j/97617951870.
Abstract: (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 t needed to ensure that every cell phone on this graph has signal strength at least r. In this talk, we define the directed (t,r) broadcast domination number of a graph and present results related to this new graph parameter.