Co-2-plex polynomials

  • Authors:
  • Benjamin Mcclosky;Anthony Simms;Illya V. Hicks

  • Affiliations:
  • Nature Source Genetics, Ithaca, USA 14850;Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, USA 21250;Computational and Applied Mathematics, Rice University, Houston, USA 77005

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2011

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Abstract

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.