A characterization of generalized cospectrality of rooted graphs with applications in graph reconstruction
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910555675033600 |
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| author | Wang, Wei Wen, Wenqiang Guo, Songlin |
| author_facet | Wang, Wei Wen, Wenqiang Guo, Songlin |
| contents | Extending a classic result of Johnson and Newman, this paper provides a matrix characterization for two generalized cospectral graphs with a pair of generalized cospectral vertex-deleted subgraphs. As an application, we present a new condition for the reconstructibility of a graph. In particular, we show that a graph with at least three vertices is reconstructible if there exists a vertex-deleted subgraph that is almost controllable and has a nontrivial automorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02488 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A characterization of generalized cospectrality of rooted graphs with applications in graph reconstruction Wang, Wei Wen, Wenqiang Guo, Songlin Combinatorics 05C50 Extending a classic result of Johnson and Newman, this paper provides a matrix characterization for two generalized cospectral graphs with a pair of generalized cospectral vertex-deleted subgraphs. As an application, we present a new condition for the reconstructibility of a graph. In particular, we show that a graph with at least three vertices is reconstructible if there exists a vertex-deleted subgraph that is almost controllable and has a nontrivial automorphism. |
| title | A characterization of generalized cospectrality of rooted graphs with applications in graph reconstruction |
| topic | Combinatorics 05C50 |
| url | https://arxiv.org/abs/2408.02488 |