Aα-Spectrum of a Firefly Graph

Q3 Computer Science

Electronic Notes in Theoretical Computer Science Pub Date : 2019-08-30 DOI:10.1016/j.entcs.2019.08.019

André Ebling Brondani, Carla Silva Oliveira, Francisca Andrea Macedo França, Leonardo de Lima

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引用次数: 6

Abstract

Let G be a connected graph of order n, A(G) is the adjacency matrix of G and D(G) is the diagonal matrix of the row-sums of A(G). In 2017, Nikiforov [Nikiforov, V., Merging the A- and Q-Spectral Theories, Applicable Analysis and Discrete Mathematics 11 (2017), pp. 81–107.] defined the convex linear combinations A_α(G) of A(G) and D(G) by $A_{α} (G) = α D (G) + (1 - α) A (G), 0 \leq α \leq 1 .$ In this paper, we obtain a partial factorization of the A_α-characteristic polynomial of the firefly graph which explicitly gives some eigenvalues of the graph.

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萤火虫图的a α-谱

设G为n阶连通图，a (G)为G的邻接矩阵，D(G)为a (G)的行和的对角矩阵。In 2017, Nikiforov, V.，合并A-和q -谱理论，应用分析与离散数学11 (2017)，pp. 81-107。定义了A(G)与D(G)的凸线性组合Aα(G)， Aα(G)=αD(G)+(1−α)A(G)，0≤α≤1。本文对萤火虫图的a α-特征多项式进行了部分分解，给出了该图的若干特征值。

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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