Coalescing sets preserving cospectrality of graphs arising from block similarity matrices
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913295334637568 |
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| author | Mahamud, Sajid Bin Butler, Steve Graff, Hannah Layman, Nick Luck, Taylor Jin, Jiah Owen, Noah Yuan, Angela |
| author_facet | Mahamud, Sajid Bin Butler, Steve Graff, Hannah Layman, Nick Luck, Taylor Jin, Jiah Owen, Noah Yuan, Angela |
| contents | Coalescing involves gluing one or more rooted graphs onto another graph. Under specific conditions, it is possible to start with cospectral graphs that are coalesced in similar ways that will result in new cospectral graphs. We present a sufficient condition for this based on the block structure of similarity matrices, possibly with additional constraints depending on which type of matrix is being considered. The matrices considered in this paper include the adjacency, Laplacian, signless Laplacian, distance, and generalized distance matrix. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01561 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coalescing sets preserving cospectrality of graphs arising from block similarity matrices Mahamud, Sajid Bin Butler, Steve Graff, Hannah Layman, Nick Luck, Taylor Jin, Jiah Owen, Noah Yuan, Angela Combinatorics Coalescing involves gluing one or more rooted graphs onto another graph. Under specific conditions, it is possible to start with cospectral graphs that are coalesced in similar ways that will result in new cospectral graphs. We present a sufficient condition for this based on the block structure of similarity matrices, possibly with additional constraints depending on which type of matrix is being considered. The matrices considered in this paper include the adjacency, Laplacian, signless Laplacian, distance, and generalized distance matrix. |
| title | Coalescing sets preserving cospectrality of graphs arising from block similarity matrices |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.01561 |