Hopping Forcing on Graphs by John Petrucci '21, Mathematics Senior Thesis Defense

Hopping Forcing on Graphs by John Petrucci ’21, Mathematics Senior Thesis Defense, Wednesday, May 5, 2:30 – 3:10 pm, live talk can be accessed at https://williams.zoom.us/j/97617951870.

Abstract:  Hopping forcing is a method used to model the spread of information throughout a graph.  Consider a graph with some vertices colored blue, and the rest colored white.  A blue vertex b can then force a white vertex w to become blue if b is not adjacent to a white vertex and has not yet forced.  We can iteratively apply this rule with the end goal of coloring every vertex in the graph blue.  The hopping forcing number of a graph is the fewest number of vertices we need to color blue at the start to eventually force the entire graph blue using hopping.  Further, we can also consider the hopping throttling number of a graph, which optimizes the sum of the size of an initial set of blue vertices and the amount of time it takes for that set to force the entire graph blue.  In this talk, we formally define these parameters and present several new results related to them.