Note on the Smallest Root of the Independence Polynomial

Source abstract

One can define the independence polynomial of a graph G as follows. Let i k (G) denote the number of independent sets of size k of G , where i 0 (G) =1. Then the independence polynomial of G is I(G,x) =∑ k =0 n (−1) k i k (G)x k . In this paper we give a new proof of the fact that the root of I(G,x) having the smallest modulus is unique and is real.