Abstract
What follows is a short, selective tour of some of the connections between weighted graphs and the group inverses of their associated Laplacian matrices. The presentation below draws heavily from Kirkland–Neumann [11, Ch. 7], and the interested reader can find further results on the topic in that book. We note that Molitierno [13] also covers some of the material presented in this chapter, and so serves as another source for readers interested in pursuing this subject further.
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Kirkland, S. (2018). The Group Inverse of the Laplacian Matrix of a Graph. In: Encinas, A., Mitjana, M. (eds) Combinatorial Matrix Theory . Advanced Courses in Mathematics - CRM Barcelona. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-70953-6_4
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DOI: https://doi.org/10.1007/978-3-319-70953-6_4
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