Abstract
The distance (signless) Laplacian eigenvalues of a connected hypergraph are the eigenvalues of its distance (signless) Laplacian matrix. For all $n$-vertex $k$-uniform hypertrees, we determine the $k$-uniform hypertree with minimum second largest distance (signless) Laplacian eigenvalue. For all $n$-vertex $k$-uniform unicyclic hypergraphs, we obtain the $k$-uniform unicyclic hypergraph with minimum largest distance (signless) Laplacian eigenvalue, and the $k$-uniform unicyclic hypergraph with minimum second largest distance Laplacian eigenvalue.
Funding Statement
This work was supported by the National Natural Science Foundation of China (No. 11871398) and China Scholarship Council (No. 202006290071).
Acknowledgments
The authors are grateful to the anonymous referees for valuable comments, suggestions and corrections which improved the presentation of this paper.
Citation
Xiangxiang Liu. Ligong Wang. "Distance (Signless) Laplacian Eigenvalues of $k$-uniform Hypergraphs." Taiwanese J. Math. 26 (6) 1093 - 1111, December, 2022. https://doi.org/10.11650/tjm/220604
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