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星图相关矩阵的Moore-Penrose广义逆
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Abstract:
本文利用矩阵的低秩性、分块性等性质给出了星图的邻接矩阵、关联矩阵、距离矩阵、拉普拉斯矩阵和无符号拉普拉斯矩阵的Moore-Penrose广义逆。以上结论对进一步研究星图的代数性质提供了理论支撑，同时对研究其他图类的相关矩阵的广义逆提供了理论参考。
Based on the properties of the low rank, partitioned matrix structure, we give the explicit form for the Moore-Penrose inverse of the adjacency matrix, incidence matrix, distance matrix, Laplacian matrix and signless-Laplacian matrix of star graphs, which provides theoretical support for further study of the algebraic properties of star graphs and theoretical aid for the study of the generalized inverse for matrices of other graphs.
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