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Signed graphs and inverses of their incidence matrices
Published 5 Nov 2023 in math.CO | (2311.02792v1)
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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