Graph Invertibility based on Drazin Invers

Autores/as

  • André Luis Andrejew Ferreira UFPel
  • Débora Marília Hauenstein UFPel
  • Guilherme Porto IFFar

Resumen

LetG= (V(G), E(G)) be a graph with vertex setV(G) ={v1, ..., vn}and edge setE(G). Inthis work, graphs may contain loops (edges that connects a vertex to itself) but no multiple edges.A weighted graph is a graph in which a number (the weight) is assigned to each edge. Let(G, w) be a weighted graph, wherew:E(G)→R\ {0}is the function that assigns weights tothe edges. The weighted adjacency matrix of (G, w) isA(G, w) = [aij], whereaij=w(vivj) ifvivj∈E(G) andaij= 0 otherwise. If the weight of each edge is equal to one thenA(G, w) is thestandard adjacency matrix of the graphG, denoted byA(G). [...]

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Citas

Campbell, S. L. and Meyer, C. D.Generalized inverses of linear transformations. Society forindustrial and applied Mathematics, 2009.

Godsil, C. D. Inverses of trees,Combinatorica, 5:33-39, 1985. DOI:10.1007/BF02579440.

McLeman, C. and McNicholas, E. Graph Invertibility.Graphs and Combinatorics, 30:977-1002, 2014. DOI:10.1007/s00373-013-1319-7.

Yang, Y. and Ye, D. Inverses of bipartite graphs.Combinatorica, 38:1251-1263, 2018. DOI:10.1007/s00493-016-3502-y.[5] Ye, D., Yang, Y., Mandal, B. and Klein, D. J. Graph invertibility and median eigenvalues,Linear Algebra and its Applications, 513:304-323, 2017. DOI:10.1016/j.laa.2016.10.020.

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Publicado

2021-12-20

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