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arXiv · 2311.02792

Signed graphs and inverses of their incidence matrices

Abdullah Alazemi·Milica Andelic·Sudipta Mallik
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Abstract

The Laplacian matrix $L$ of a signed graph $G$ may or may not be invertible. We present a combinatorial formula of the Moore-Penrose inverse of $L$. This is achieved by finding a combinatorial formula for the Moore-Penrose inverse of an incidence matrix of $G$. This work generalizes related known results on incidence and Laplacian matrices of an unsigned graph. Several examples are provided to show the usefulness of these combinatorial formulas.

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Abdullah Alazemi, Milica Andelic, Sudipta Mallik. 2023-11-05. Signed graphs and inverses of their incidence matrices. https://arxiv.org/abs/2311.02792

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