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On unimodular graphs

Akbari, S ; Sharif University of Technology | 2007

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  1. Type of Document: Article
  2. DOI: 10.1016/j.laa.2006.10.017
  3. Publisher: 2007
  4. Abstract:
  5. We study graphs whose adjacency matrices have determinant equal to 1 or -1, and characterize certain subclasses of these graphs. Graphs whose adjacency matrices are totally unimodular are also characterized. For bipartite graphs having a unique perfect matching, we provide a formula for the inverse of the corresponding adjacency matrix, and address the problem of when that inverse is diagonally similar to a nonnegative matrix. Special attention is paid to the case that such a graph is unicyclic. © 2006 Elsevier Inc. All rights reserved
  6. Keywords:
  7. Matrix algebra ; Numerical methods ; Problem solving ; Determinant ; Minor ; Unicyclic graph ; Unimodular graph ; Graph theory
  8. Source: Linear Algebra and Its Applications ; Volume 421, Issue 1 , 2007 , Pages 3-15 ; 00243795 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0024379506004708