Odd Wheels Are Not Odd-Distance Graphs

An odd wheel graph is a graph formed by connecting a new vertex to all vertices of an odd cycle. We answer a question of Rosenfeld and Le by showing that odd wheels cannot be drawn in the plane so that the lengths of the edges are odd integers

Every Graph is an Integral Distance Graph in the Plane

We prove that every finite simple graph can be drawn in the plane so that any two vertices have an integral distance if and only if they are adjacent. The proof is constructive.