Orbit Polynomial of Graphs versus Polynomial with Integer Coefficients

Ghorbani, Modjtaba; Jalali-Rad, Maryam; Dehmer, Matthias

doi:10.3390/sym13040710

Cited by 4 publications

(1 citation statement)

References 25 publications

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“…The automorphism group of this graph is S 1 , which implies that O F (x) = 115x and O F (x) = 1 − 115x, which yield that δ = 0.008. In Table 1, some results including the sizes of the networks, the orders of the automorphism groups, and the positive roots of the modified orbit polynomials [22] are summarized. In this table, the symbol δ denotes the unique positive root of the modified orbit polynomial.…”

Section: Application In Real-world Networkmentioning

confidence: 99%

Network Analyzing by the Aid of Orbit Polynomial

Ghorbani

Dehmer

2021

Symmetry

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This article aims to be a further contribution to the research on structural complexity networks. Here, we emphasize measures to determine symmetry. The so-called “orbit polynomial” is defined by OG(x)=∑iaixi, where ai is the number of orbits of size i. Furthermore, the graph polynomial 1−OG(x) has a unique positive root in the interval (0,1), which can be considered as a relevant measure of the symmetry of a graph. In the present paper, we studied some properties of the orbit polynomial with respect to the stabilizer elements of each vertex. Furthermore, we constructed graphs with a small number of orbits and characterized some classes of graphs in terms of calculating their orbit polynomials. We studied the symmetry structure of well-known real-world networks in terms of the orbit polynomial.

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Section: Application In Real-world Networkmentioning

confidence: 99%