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https://www.um.edu.mt/library/oar/handle/123456789/65145
Title: | The walks and CDC of graphs with the same main eigenspace |
Authors: | Sciriha, Irene Collins, Luke |
Keywords: | Eigenvalues Mathematics Graphic methods |
Issue Date: | 2021 |
Publisher: | Sciendo |
Citation: | Sciriha, I., & Collins, L. (2021). The walks and CDC of graphs with the same main eigenspace. Discussiones Mathematicae Graph Theory, 1-26. |
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. |
URI: | https://www.um.edu.mt/library/oar/handle/123456789/65145 |
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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