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Commutativity of the adjacency matrices of graphs

Akbari, S ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1016/j.disc.2008.09.006
  3. Publisher: 2009
  4. Abstract:
  5. We say that two graphs G1 and G2 with the same vertex set commute if their adjacency matrices commute. In this paper, we find all integers n such that the complete bipartite graph Kn, n is decomposable into commuting perfect matchings or commuting Hamilton cycles. We show that there are at most n - 1 linearly independent commuting adjacency matrices of size n; and if this bound occurs, then there exists a Hadamard matrix of order n. Finally, we determine the centralizers of some families of graphs. © 2008 Elsevier B.V. All rights reserved
  6. Keywords:
  7. Adjacency matrix ; Commutativity ; Complete bipartite graphs ; Graph decomposition ; Hadamard matrices ; Hamilton cycles ; Perfect matchings ; Two-graphs ; Vertex sets ; Graph theory
  8. Source: Discrete Mathematics ; Volume 309, Issue 3 , 2009 , Pages 595-600 ; 0012365X (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0012365X08005359