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Moore–Penrose inverse of incidence matrix of graphs with complete and cyclic blocks
Let Γ be a graph with n vertices, where each edge is given an orientation and let Q be the vertex–edge incidence matrix of Γ. Suppose that Γ has a cut-vertex v and Γ−v=Γ[V1]∪Γ[V2]. We obtain a relation between the Moore–Penrose inverse of the incidence matrix of Γ and of the incidence matrices of th...
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Published in: | Discrete mathematics 2019-01, Vol.342 (1), p.10-17 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | Let Γ be a graph with n vertices, where each edge is given an orientation and let Q be the vertex–edge incidence matrix of Γ. Suppose that Γ has a cut-vertex v and Γ−v=Γ[V1]∪Γ[V2]. We obtain a relation between the Moore–Penrose inverse of the incidence matrix of Γ and of the incidence matrices of the induced subgraphs Γ[V1∪{v}] and Γ[V2∪{v}]. The result is used to give a combinatorial interpretation of the Moore–Penrose inverse of the incidence matrix of a graph whose blocks are either cliques or cycles. Moreover we obtain a description of minors of the Moore–Penrose inverse of the incidence matrix when the rows are indexed by cut-edges. The results generalize corresponding results for trees in the literature. |
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ISSN: | 0012-365X 1872-681X |
DOI: | 10.1016/j.disc.2018.09.020 |