cone over a graph

Let $G = (V, E)$ be a simple graph with edges numbered 1 through $n$ . The cone over $G$ is defined to be the graph $G^{+} = (V \cup {0}, E^{+})$ where $E^{+} = E \cup {(0, i) ∣ i \in [n]}$ .
In other words, we add one more vertex $0$ and draw an edge from 0 to every other element.