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Czechoslovak Mathematical Journal, Vol. 70, No. 3, pp. 605-629, 2020

On sectional Newtonian graphs

Zening Fan, Suo Zhao

Received February 7, 2020.   Published online August 17, 2020.
Abstract:  In this paper, we introduce the so-called sectional Newtonian graphs for univariate complex polynomials, and study some properties of those graphs. In particular, we list all possible sectional Newtonian graphs when the degrees of the polynomials are less than five, and also show that every stable gradient graph can be realized as a polynomial sectional Newtonian graph.
Keywords:  sectional Newtonian graph; level set; partition
Classification MSC:  05C75, 53C43
DOI:  10.21136/CMJ.2020.0049-20
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Affiliations:   Zening Fan, College of Mathematics, Sichuan University, No.24 South Section 1 Yihuan Road, Chengdu 610064, P. R. China, e-mail: zeningfan@126.com; Suo Zhao (corresponding author), Jiajia Research Center, Shanghai Yuanlu Jiajia Information & Technology Co., Ltd., No.1166 Shuangqiao Road, Shanghai 201208, P. R. China, e-mail: saaki@163.com
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