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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