The Geodetic Domination Number for the Product of Simple Graphs

Abstract

Let G=(V,E) be an undirected graph, simple, finite and connected graph. Domination in graphs has been an extensively researched branch of graph theory. Viewing a graph as a category whose objects are the vertices and whose morphisms are the paths in the graph, the cartesian product of graphs corresponds to the funny tensor product of categories. The cartesian product of graphs is one of two graph products that turn the category of graphs and graph homomorphisms into a symmetric closed monoidal category (as opposed to merely symmetric monoidal), the other being the tensor product of graphs. The internal hom [G,H] for the cartesian product of graphs has graph homomorphisms from G to H as vertices and "unnatural transformations" between them as edges..