The Common Neighborhood Graph and Its Energy

Let G be a simple graph with vertex set {v1, v2, . . . ,vn}. The common neighborhood graph (congraph) of G, denoted by con(G), is the graph with vertex set {v1, v2, . . . , vn}, in which two vertices are adjacent if and only they have at least one common neighbor in the graph G. The basic properties of con(G) and of its energy are established.