Binary codes from graphs have been studied widely since 1960’s. Matrices associated with the graphs were considered as a good tool to construct codes from graphs. Incidence matrix, adjacency matrix, cut set matrix, circuit matrix, etc. were widely used to construct codes with desirable properties. We introduce a binary code called the vertex code C from a given graph G, depending on the degree of the vertices of G, in such a way that the vertex polynomial of G is same as the weight enumerator of C, and determine the vertex codes for certain classes of graphs. The graphs resulting from the Cartesian product of these graphs are dealt with.

graph, binary code, Cartesian product, vertex code, vertex polynomial.