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Keywords:

  • expected independence polynomial;
  • graph;
  • roots

Abstract

The independence polynomial of a (finite) graph is the generating function for the number of independent sets of each cardinality. Assuming that each possible edge of a complete graph of order n is independently operational with probability p, we consider the expected independence polynomial. We show here that for all fixed inline image, the expected independence polynomials of complete graphs have all real, simple roots.