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DC Field | Value | Language |
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dc.contributor.author | Sciriha, Irene | - |
dc.contributor.author | Collins, Luke | - |
dc.date.accessioned | 2020-12-03T09:49:49Z | - |
dc.date.available | 2020-12-03T09:49:49Z | - |
dc.date.issued | 2021 | - |
dc.identifier.citation | Sciriha, I., & Collins, L. (2021). The walks and CDC of graphs with the same main eigenspace. Discussiones Mathematicae Graph Theory, 1-26. | en_GB |
dc.identifier.uri | https://www.um.edu.mt/library/oar/handle/123456789/65145 | - |
dc.description.abstract | The main eigenvalues of a graph G are those eigenvalues of the (0, 1)-adjacency matrix A with a corresponding eigenspace not orthogonal to j = (1 | 1 | · · · | 1)T. The principal main eigenvector associated with a main eigenvalue is the orthogonal projection of the corresponding eigenspace onto j. The main eigenspace of a graph is generated by all the principal main eigenvectors and is the same as the image of the walk matrix. We explore a new concept to see to what extent the main eigenspace determines the entries of the walk matrix of a graph. The CDC of a graph G is the direct product G × K2. We establish a hierarchy of inclusions connecting classes of graphs in view of their CDC, walk matrix, main eigenvalues and main eigenspaces. We provide a new proof that graphs with the same CDC are characterized as TF-isomorphic graphs. A complete list of TF-isomorphic graphs on at most 8 vertices and their common CDC is also given. | en_GB |
dc.language.iso | en | en_GB |
dc.publisher | Sciendo | en_GB |
dc.rights | info:eu-repo/semantics/openAccess | en_GB |
dc.subject | Eigenvalues | en_GB |
dc.subject | Mathematics | en_GB |
dc.subject | Graphic methods | en_GB |
dc.title | The walks and CDC of graphs with the same main eigenspace | en_GB |
dc.type | article | en_GB |
dc.rights.holder | The copyright of this work belongs to the author(s)/publisher. The rights of this work are as defined by the appropriate Copyright Legislation or as modified by any successive legislation. Users may access this work and can make use of the information contained in accordance with the Copyright Legislation provided that the author must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the prior permission of the copyright holder. | en_GB |
dc.description.reviewed | peer-reviewed | en_GB |
dc.identifier.doi | 10.7151/dmgt.2386 | - |
dc.publication.title | Discussiones Mathematicae Graph Theory | - |
Appears in Collections: | Scholarly Works - FacSciMat |
Files in This Item:
File | Description | Size | Format | |
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The_walks_and_CDC_of_graphs_with_the same_main_eigenspace_2021.pdf | 998.89 kB | Adobe PDF | View/Open |
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