计算森林的拉普拉斯系数

J. Appl. Math. Pub Date : 2022-10-22 DOI:10.1155/2022/8199547

A. Ghalavand, A. Ashrafi

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In an earlier paper, the coefficients \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\n <msub>\n <mrow>\n <mi>c</mi>\n </mrow>\n <mrow>\n <mi>n</mi>\n <mo>−</mo>\n <mn>4</mn>\n </mrow>\n </msub>\n </math>\n and \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\n <msub>\n <mrow>\n <mi>c</mi>\n </mrow>\n <mrow>\n <mi>n</mi>\n <mo>−</mo>\n <mn>5</mn>\n </mrow>\n </msub>\n </math>\n for forests with respect to some degree-based graph invariants were computed. The aim of this paper is to continue this work by giving an exact formula for the coefficient \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\n <msub>\n <mrow>\n <mi>c</mi>\n </mrow>\n <mrow>\n <mi>n</mi>\n <mo>−</mo>\n <mn>6</mn>\n </mrow>\n </msub>\n </math>\n .","PeriodicalId":14766,"journal":{"name":"J. Appl. 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引用次数: 0

摘要

设G是一个具有拉普拉斯多项式ψ G的有限简单图，λ =∑k = 0 n−1 n−kck λ k。在之前的一篇论文中，系数c n - 4和c对一些基于度的图不变量计算了森林的N−5。本文的目的是通过给出系数cn - 6的精确公式来继续这项工作。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Computing some Laplacian Coefficients of Forests

Let

G

be a finite simple graph with Laplacian polynomial

ψ (G, λ) = \sum_{k = 0}^{n} {(- 1)}^{n - k} c_{k} λ^{k}

. In an earlier paper, the coefficients

c_{n - 4}

and

c_{n - 5}

for forests with respect to some degree-based graph invariants were computed. The aim of this paper is to continue this work by giving an exact formula for the coefficient

c_{n - 6}

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J. Appl. Math.

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