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On $$\sigma$$-polynomials. (English) Zbl 0658.05025
This paper discusses properties of $$\sigma$$-polynomials (which are closely related to chromatic polynomials in factorial form), and characterizes those that are quadratic. The number of graphs with a given quadratic $$\sigma$$-polynomials is derived, as well as the number of quadratic $$\sigma$$-polynomials, $$\sigma^ 2+a\sigma +b$$, for a given a.