Abstract
The edge cover polynomial of a graph G is the function E(G,x)=∑i≥1e(G,i)xi, where e(G,i) is the number of edge coverings of G with size i. In this paper, we show that the average edge cover polynomial of order n is reduced to the edge cover polynomial of complete graph Kn, based on which we establish that the average edge cover polynomial of order n is unimodal and has at least n−3 non-real roots.
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