Open AccessGroup inverses of matrices associated with certain graph classes
Author(s) -
Judith J. McDonald,
Raju Nandi,
K. C. Sivakumar
Publication year - 2022
Publication title -
the electronic journal of linear algebra
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.447
H-Index - 31
eISSN - 1537-9582
pISSN - 1081-3810
DOI - 10.13001/ela.2022.6717
Subject(s) - adjacency matrix , mathematics , bipartite graph , combinatorics , inverse , complete bipartite graph , discrete mathematics , integer matrix , graph , symmetric matrix , nonnegative matrix , eigenvalues and eigenvectors , geometry , physics , quantum mechanics
We obtain formulae for group inverses of matrices that are associated with a new class of digraphs obtained from stars. This new class contains both bipartite and non-bipartite graphs. Expressions for the group inverse of matrices corresponding to double star digraphs and the adjacency matrix of certain undirected multi-star graphs are also proven. A blockwise representation of the inverse or group inverse of the adjacency matrix of the Dutch windmill graph is presented.