Williams, Gerald (2014) Smith forms for adjacency matrices of circulant graphs. Linear Algebra and its Applications, 443. pp. 21-33. DOI https://doi.org/10.1016/j.laa.2013.11.006
Williams, Gerald (2014) Smith forms for adjacency matrices of circulant graphs. Linear Algebra and its Applications, 443. pp. 21-33. DOI https://doi.org/10.1016/j.laa.2013.11.006
Williams, Gerald (2014) Smith forms for adjacency matrices of circulant graphs. Linear Algebra and its Applications, 443. pp. 21-33. DOI https://doi.org/10.1016/j.laa.2013.11.006
Abstract
We calculate the Smith normal form of the adjacency matrix of each of the following graphs or their complements (or both): complete graph, cycle graph, square of the cycle, power graph of the cycle, distance matrix graph of cycle, Andrásfai graph, Doob graph, cocktail party graph, crown graph, prism graph, Möbius ladder. The proofs operate by finding the abelianization of a cyclically presented group whose relation matrix is column equivalent to the required adjacency matrix.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Smith normal form; Circulant graph; Adjacency matrix |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
| SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
| Depositing User: | Unnamed user with email elements@essex.ac.uk |
| Date Deposited: | 07 Jan 2014 11:32 |
| Last Modified: | 30 Oct 2024 20:43 |
| URI: | http://repository.essex.ac.uk/id/eprint/8578 |
Available files
Filename: SNRcirculantgraphs.pdf