Abstract by Joshua Faught
Resistance Distance in Flower Graphs
Resistance distance is a form of metric on connected graphs that becomes exponentially difficult to compute as the size of a graph increases. We examine the resistance distance on a class of graphs that may be decomposed into chains of some graph G and derive a generalized formula for the resistance between any two vertices. We apply this formula to a subclass of these graphs, named flower graphs, and proceed to give an explicit formula for Kemeny's constant and the Kirchhoff index of these flower graphs.