Exponential Domination in Grids

Domination in graphs has been an important and active topic in graph theory for over 40 years. It has immediate applications in visibility and controllability. In this talk we will discuss a generalization of domination called exponential dom- ination. A vertex v in an exponential dominating set assigns weight 21−dist(v,u) to vertex u. An exponential dominating set of a graph G is a subset of V (G) such that every vertex in V (G) has been assigned a sum weight of at least 1. We will specifically look at grid graphs and graphs on the torus.

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