有向图的复无符号拉普拉斯矩阵的摩尔 - 彭罗斯逆的组合公式
Combinatorial formula for the Moore-Penrose inverse of the complex signless Laplacian of an oriented graph
浏览论文内容
中文总结 AI 辅助
研究具有非零复边权重的弱连通有向图，通过找到无符号关联矩阵秩的充要条件，得出复无符号关联矩阵和复无符号拉普拉斯矩阵的摩尔 - 彭罗斯逆的组合公式，解决了相关开放问题。
中文摘要 AI 辅助
我们找到了具有非零复边权重的弱连通有向图的无符号关联矩阵秩的充要条件。利用此条件，我们得出了具有非零复边权重的弱连通有向图的复无符号关联矩阵和复无符号拉普拉斯矩阵的摩尔 - 彭罗斯逆的组合公式。这解决了Barik等人在论文结尾提出的开放问题。
英文摘要
We find necessary and sufficient conditions for the rank of the signless incidence matrix of a weakly connected oriented graph with non-zero complex edge weights. We use this to find the combinatorial formulas for the Moore-Penrose inverse of the complex signless incidence and complex signless Laplacian matrix of a weakly connected oriented graph with non-zero complex edge weights. This resolves the open problem posed in the concluding remarks of Barik et. al. (Discrete Mathematics 349 (9), 115117, 2026).
