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Main Author: Saha, Shib Sankar
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2603.14048
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author Saha, Shib Sankar
author_facet Saha, Shib Sankar
contents Let $\mathcal{S}(\mathcal{H})$ be the Seidel matrix of a hypergraph $\mathcal{H}$, and the Seidel energy is denoted by the sum of the absolute eigenvalues of $\mathcal{S}(\mathcal{H})$. In [G.~X.~Tian, Y.~Li and S.~Y.~Cui, The change of Seidel energy of tripartite Turán graph due to edge deletion, Linear Multilinear Algebra, 19 (2022), 4597-4614] and [Y.~Liu, X.~Chen, The change of Seidel energy of 5-partite Turán graph due to edge deletion, Discrete Applied Mathematics, 2024, 342, 104-123], the authors studied the change of Seidel energy of the Turán graph due to edge deletion. In this article, we analyze the Seidel spectrum of the complete $3$-uniform bipartite hypergraph $\mathcal{C}^3_{m,n}$ and show that it has exactly one negative Seidel eigenvalue even after a single hyperedge deletion. Finally, we prove that the Seidel energy of the complete $3$-uniform bipartite hypergraph $\mathcal{C}^3_{m,n}$ decreases after single hyperedge and vertex deletion for all $m,n \ge 3$.
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publishDate 2026
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spellingShingle On the Seidel energy of uniform hypergraphs due to hyperedge and vertex deletion
Saha, Shib Sankar
Combinatorics
Let $\mathcal{S}(\mathcal{H})$ be the Seidel matrix of a hypergraph $\mathcal{H}$, and the Seidel energy is denoted by the sum of the absolute eigenvalues of $\mathcal{S}(\mathcal{H})$. In [G.~X.~Tian, Y.~Li and S.~Y.~Cui, The change of Seidel energy of tripartite Turán graph due to edge deletion, Linear Multilinear Algebra, 19 (2022), 4597-4614] and [Y.~Liu, X.~Chen, The change of Seidel energy of 5-partite Turán graph due to edge deletion, Discrete Applied Mathematics, 2024, 342, 104-123], the authors studied the change of Seidel energy of the Turán graph due to edge deletion. In this article, we analyze the Seidel spectrum of the complete $3$-uniform bipartite hypergraph $\mathcal{C}^3_{m,n}$ and show that it has exactly one negative Seidel eigenvalue even after a single hyperedge deletion. Finally, we prove that the Seidel energy of the complete $3$-uniform bipartite hypergraph $\mathcal{C}^3_{m,n}$ decreases after single hyperedge and vertex deletion for all $m,n \ge 3$.
title On the Seidel energy of uniform hypergraphs due to hyperedge and vertex deletion
topic Combinatorics
url https://arxiv.org/abs/2603.14048