Co‐2‐plex polynomials

This paper offers a generalization of the independence polynomial, the co‐k‐plex polynomial. The resulting family of polynomials carries combinatorial information on a class of independence systems defined over the vertex set of a finite graph. Specifically, we offer a recursion formula and examples of the co‐2‐plex polynomial on certain graphs. In addition, we characterize the class of graphs whose co‐2‐plex polynomial will have all real roots.