MegaMenger Graphs. (1st January 2018) - Bickle, Allan
Summary: In 2014, faculty and students at colleges around the world participated in the MegaMenger project to build a model of the Menger sponge, a type of fractal, out of business cards. This model can itself be modeled using graph theory, with each vertex representing a small cube and an edge between two vertices whenever they share a face. We determine the order, size, and partite set sizes of graphs representing different steps of building the Menger sponge and Sierpinski carpet, along with the surface area of the Menger sponge. Many results involve recurrence relations, which we work through in some detail.