Randić 矩阵

简单图的 Randić 矩阵是一个加权邻接矩阵，其权重为

(1)

其中是图的顶点度。换句话说，

$[A_(Randic)]_(ij)={1/(sqrt(d_id_j)) for i,j adjacent; 0 otherwise$

(2)

(Zheng et al. 2022)。

Randić 矩阵的最大特征值对于空图为 0，否则为 1，这意味着其谱半径是微不足道的。Randić 矩阵的矩阵元素之和的一半是 Randić 指数，其特征值的绝对值之和是 Randić 能量。

另请参阅

Randić 能量, Randić 指数, Randić 谱半径, 加权邻接矩阵

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参考文献

Bozkurt, S. B. and Guüngör, A. D. "Randić Matrix and Randić Energy." MATCH Commun. Math. Comput. Chem. 64, 239-250, 2010.Bozkurt, S. B.; Guüngör, A. D.; and Gutman, I. "Randić Spectral Radius and Randić Energy." MATCH Commun. Math. Comput. Chem. 64, 321-334, 2010.Randić, M. "On Characterization of Molecular Branching." J. Amer. Chem. Soc. 97, 6609-6615, 1975.Rodríguez, J. A. "A Spectral Approach to the Randić Index." Linear Algebra Appl. 400, 339-344, 2005.Rodríguez, J. A. and Sigarreta, J. M. "On the Randić Index and Conditional Parameters of a Graph." MATCH Commun. Math. Comput. Chem. 54, 403-416, 2005.Zheng, R.; Su, P.; and Jin. S. "Arithmetic-Geometric Matrix of Graphs and Its Applications." Appl. Math. Comput. 42, 127764, 1-11, 2023.

请引用为

Weisstein, Eric W. “Randić 矩阵。” 来自 MathWorld--Wolfram Web 资源。https://mathworld.net.cn/RandicMatrix.html