Let \(G\) be a graph with \(n\) vertices. The vertex matching polynomial \(M_v(G, x)\) of the graph \(G\) is defined as the sum of \((-1)^rq_v(G,r)x^{n-r}\), in which \(q_v(G,r)\) is the number of \(r\)-vertex independent sets. In this paper, we extend some important properties of the matching polynomial to the vertex matching polynomial \(M_v(G,2x)\). The matching and vertex matching polynomials of some important class of graphs and some applications in nanostructures are presented.