Multidegrees of Binomial Edge Ideals

A binomial edge ideal is a type of ideal that we can generate using a simple, connected graph. We prove how to calculate the multidegree of a binomial edge ideal based on combinatorial properties of the underlying graph. In particular, we study the collection of subsets of vertices whose prime ideals have minimum codimension. We provide results which assist in determining these subsets, then find these collections for star, horned complete, barbell, cycle, wheel, and friendship graphs, and use the main result of the paper to obtain the multidegrees of their binomial edge ideals.