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arXiv · 2509.12342

Spectra of T-vertex and T-edge neighbourhood corona of Two Graphs

Indranil Mukherjee·Suvra Kanti Chakraborty·Arpita Das
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Abstract

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.

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Indranil Mukherjee, Suvra Kanti Chakraborty, Arpita Das. 2025-09-15. Spectra of T-vertex and T-edge neighbourhood corona of Two Graphs. https://arxiv.org/abs/2509.12342

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