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A Study of Roots of a Certain Class of Counting Polynomials
Version 1
: Received: 10 May 2023 / Approved: 10 May 2023 / Online: 10 May 2023 (10:25:39 CEST)
A peer-reviewed article of this Preprint also exists.
Ghorbani, M.; Alidehi-Ravandi, R.; Dehmer, M.; Emmert-Streib, F. A Study of Roots of a Certain Class of Counting Polynomials. Mathematics 2023, 11, 2876. Ghorbani, M.; Alidehi-Ravandi, R.; Dehmer, M.; Emmert-Streib, F. A Study of Roots of a Certain Class of Counting Polynomials. Mathematics 2023, 11, 2876.
Abstract
Suppose G is a graph with vertex-orbits O1,1 O2, . . . ,Ot, and jOi j denotes the cardinallity
of Oi. Then OG (x) = åt
2 i=1 xjOi j is called as orbit polynomial. It is well-known that this polynomial
3 has a unique positive zero d in the interval [0, 1]. The aim of this paper is to study the specific
4 properties of this polynomial and then we determine the location of this root for several classes of
5 complex networks to compare with other graphical measures. Besides, we compare the unique
6 positive zero measure with several well-known centrality graph measures.
Keywords
orbit polynomial; complex networks; automorphism group; entropy
Subject
Computer Science and Mathematics, Discrete Mathematics and Combinatorics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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