Signed graphs and inverses of their incidence matrices

Abdullah Alazemi; Milica Andelic; Sudipta Mallik

Signed graphs and inverses of their incidence matrices

Combinatorics 2023-11-07 v1

Authors: Abdullah Alazemi , Milica Andelic , Sudipta Mallik

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.

Keywords

signed graphs laplacian matrix incidence matrix moore-penrose inverse combinatorial formula

Cite

@article{arxiv.2311.02792,
  title  = {Signed graphs and inverses of their incidence matrices},
  author = {Abdullah Alazemi and Milica Andelic and Sudipta Mallik},
  journal= {arXiv preprint arXiv:2311.02792},
  year   = {2023}
}

Comments

20 pages

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