Orthogonal polynomials through complex matrix graph theory

Balasubramanian, K.

doi:10.1007/s10910-022-01415-x

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2023

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“…Hosoya was the first chemist that introduced the Hosoya counting polynomial (Cpolynomial) [2] and other well-known C-polynomials that have been defined to date, which can be found in references [3][4][5][6][7] as well as [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Orbit Polynomial of Graphs versus Polynomial with Integer Coefficients

2021

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Suppose ai indicates the number of orbits of size i in graph G. A new counting polynomial, namely an orbit polynomial, is defined as OG(x) = ∑i aixi. Its modified version is obtained by subtracting the orbit polynomial from 1. In the present paper, we studied the conditions under which an integer polynomial can arise as an orbit polynomial of a graph. Additionally, we surveyed graphs with a small number of orbits and characterized several classes of graphs with respect to their orbit polynomials.

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