| 两类六角系统的$Aalpha$-特征多项式和$Aalpha$-谱 |
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| 引用本文： | 袁梦玥,文飞,王冉冉. 两类六角系统的$Aalpha$-特征多项式和$Aalpha$-谱[J]. 数学研究及应用, 2023, 43(3): 266-276 |
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| 作者姓名： | 袁梦玥 文飞 王冉冉 |
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| 作者单位： | 兰州交通大学应用数学研究所, 甘肃 兰州 730070 |
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| 基金项目： | 国家自然科学基金(Grant No.11961041),甘肃省自然科学基金(Grant No.21JR11RA065),甘肃省教育厅优秀研究生“创新之星”项目(Grant No.2021CXZX-594). |
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| 摘 要： | 2017年, Nikiforov首次提出研究图$G$的$Aalpha$-矩阵, 其定义为:$Aalpha(G)=alpha D(G)+(1-alpha)A(G) (alphain [0,1])$, 其中$A(G)$和$D(G)$分别为图$G$的邻接矩阵和度对角矩阵. 设$F_n$和$M_n$分别为圈状六角系统和M"{o}bius带状六角系统图. 根据循环矩阵的行列式和特征值, 本文首先给出图$F_n$和$M_n$的$Aalph$-特征多项式和$Aalpha$-谱, 进一步得到图$F_n$和$M_n$的$Aalpha$-能量的上界.
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| 关 键 词： | $Aalpha$-特征多项式 $Aalpha$-谱 六角系统 |
| 收稿时间： | 2022-04-28 |
| 修稿时间： | 2022-08-22 |
On the $A_{alpha}$-Characteristic Polynomials and the $A_{alpha}$-Spectra of Two Classes of Hexagonal Systems |
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| Mengyue YUAN,Fei WEN,Ranran WANG. On the $A_{alpha}$-Characteristic Polynomials and the $A_{alpha}$-Spectra of Two Classes of Hexagonal Systems[J]. Journal of Mathematical Research with Applications, 2023, 43(3): 266-276 |
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| Authors: | Mengyue YUAN Fei WEN Ranran WANG |
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| Affiliation: | Institute of Applied Mathematics, Lanzhou Jiaotong University, Gansu 730070, P. R. China |
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| Abstract: | The $A_{alpha}$-matrix of a graph $G$ is defined as $A_{alpha}(G)=alpha D(G)+(1-alpha)A(G)$ $(alphain[0,1])$, given by Nikiforov in 2017, where $A(G)$ and $D(G)$ are, respectively, the adjacency matrix and the degree matrix of graph $G$. Let $F_{n}$ and $M_{n}$ be hexacyclic system graph and M"{o}bius hexacyclic system graph, respectively. In this paper, according to the determinant and the eigenvalues of a circulant matrix, we firstly present $A_{alpha}$-characteristic polynomial and $A_{alpha}$-spectrum of $F_{n}$ (resp., $M_{n}$). Furthermore, we obtain the upper bound of the $A_{alpha}$-energy of $F_{n}$ (resp., $M_{n}$). |
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| Keywords: | $A_{alpha}$-characteristic polynomial $A_{alpha}$-spectrum hexagonal system |
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