Clique polynomials have a unique root of smallest modulus
نویسندگان
چکیده
Given an undirected graph G, let PG(z) be the polynomial PG(z) = ∑ n (−1)ncnz , where cn is the number of cliques of size n in G. We show that, for every G, the polynomial PG(z) has only one root of smallest modulus. Clique polynomials are related to trace monoids. Indeed, 1 PG(z) is the generating function of the sequence {tn}, where tn is the number of traces of size n in the trace monoid defined by G. Our result can be applied to derive asymptotic expressions for {tn} and other sequences arising from the analysis of algorithms for the recognition of trace languages.
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عنوان ژورنال:
- Inf. Process. Lett.
دوره 75 شماره
صفحات -
تاریخ انتشار 2000