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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.12342 |
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| _version_ | 1866918141541482496 |
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| author | Mukherjee, Indranil Chakraborty, Suvra Kanti Das, Arpita |
| author_facet | Mukherjee, Indranil Chakraborty, Suvra Kanti Das, Arpita |
| contents | The $T$-graph $T(G)$ of a graph $G$ is the graph whose vertices are the vertices and edges of $G$, with two vertices of $T(G)$ are adjacent if and only if the corresponding elements of $G$ are adjacent or incident. In this paper, we determine the adjacency and Laplacian spectra of $T$-vertex neighborhood corona and $T$-edge neighborhood corona of a connected regular graph with an arbitrary regular graph in terms of their eigenvalues. Moreover, applying these results we construct some non-regular $A$-cospectral and $L$-cospectral graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12342 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectra of T-vertex and T-edge neighbourhood corona of Two Graphs Mukherjee, Indranil Chakraborty, Suvra Kanti Das, Arpita Combinatorics 05C50 The $T$-graph $T(G)$ of a graph $G$ is the graph whose vertices are the vertices and edges of $G$, with two vertices of $T(G)$ are adjacent if and only if the corresponding elements of $G$ are adjacent or incident. In this paper, we determine the adjacency and Laplacian spectra of $T$-vertex neighborhood corona and $T$-edge neighborhood corona of a connected regular graph with an arbitrary regular graph in terms of their eigenvalues. Moreover, applying these results we construct some non-regular $A$-cospectral and $L$-cospectral graphs. |
| title | Spectra of T-vertex and T-edge neighbourhood corona of Two Graphs |
| topic | Combinatorics 05C50 |
| url | https://arxiv.org/abs/2509.12342 |