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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.
Reviewer: R.C.Read

MSC:
05C15 Coloring of graphs and hypergraphs
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References:
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[2] Frucht, R.W.; Giudici, R.E., Some chromatically unique graphs with seven points, Ars combin., 16-A, 161-172, (1983) · Zbl 0536.05026
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[4] Dhurandhar, M., Characterization of quadratic and cubic σ-polynomials, J. combin. theory ser. B, 37, 210-220, (1984) · Zbl 0554.05030
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