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Determinantal properties of Boolean graphs using recursive approach
- Source :
- AKCE International Journal of Graphs and Combinatorics, Vol 21, Iss 1, Pp 16-22 (2024)
- Publication Year :
- 2024
- Publisher :
- Taylor & Francis Group, 2024.
-
Abstract
- AbstractThe aim of this paper is to study the determinant and inverse of the adjacency matrices of weighted and directed versions of Boolean graphs. Our approach is recursive. We describe the adjacency matrix of a weighted Boolean graph in terms of the adjacency matrix of a smaller-sized weighted Boolean graph. This allows us to compute the determinant and inverse of the adjacency matrix of a weighted Boolean graph recursively. In particular, we show that the determinant of a directed Boolean graph is 1. Further, using a classical theorem of Cayley which expresses the determinant of any skew-symmetric matrix as a square of its Pfaffian, we show that for any directed Boolean graph, the characteristic polynomial has all its even degree coefficients strictly positive with the odd ones being zero.
Details
- Language :
- English
- ISSN :
- 09728600 and 25433474
- Volume :
- 21
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- AKCE International Journal of Graphs and Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.b8eb43a6026e48fd80c0f856dce8072c
- Document Type :
- article
- Full Text :
- https://doi.org/10.1080/09728600.2023.2240865