Dokažemo, da imajo rodovni polinomi grafov, imenovanih iterirane klešče, realne korene. To je nadaljevanje našega dela usmerjenega k 25 let stari domnevi, da je rodovna porazdelitev vsakega grafa ...log-konkavna. Pokazali smo že log-konkavnost za zaporedja grafov, konstruiranih z iterativno vozliščno amalgamacijo ali iterativno povezavno amalgamacijo grafov, ki zadoščajo zelo splošnemu pogoju glede njihovih particioniranih rodovnih porazdelitev, čeprav je bilo predhodno dokazano, da iterativna amalgamacija ne ohranja vselej realnosti korenov rodovnega polinoma iteriranega grafa. V tem članku je iterirana topološka operacija dodajanje klešč, ne pa vozliščna ali povezavna amalgamacija. Naša tukajšnja analiza ilustrira nekaj prednosti uporabe matrične reprezentacije transpozicije množice produkcij.
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