Multidegrees of binomial edge ideals

Let G be a simple graph with binomial edge ideal JG. We prove how to calculate the multidegree of JG based on combinatorial properties of G. In particular, we study the set Sₘᵢₙ(G) defined as the collection of subsets of vertices whose prime ideals have minimum codimension. We provide results which assist in determining Sₘᵢₙ(G), then calculate Sₘᵢₙ(G) 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.