Geodesic
Sharp lower bounds on the spectral radius of uniform hypergraphs concerning degrees
Liying Kang1 ; Lele Liu1 ; Erfang Shan1
1Shanghai University
The electronic journal of combinatorics, Tome 25 (2018) no. 2
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Let $\mathcal{A}(H)$ and $\mathcal{Q}(H)$ be the adjacency tensor and signless Laplacian tensor of an $r$-uniform hypergraph $H$. Denote by $\rho(H)$ and $\rho(\mathcal{Q}(H))$ the spectral radii of $\mathcal{A}(H)$ and $\mathcal{Q}(H)$, respectively. In this paper we present a lower bound on $\rho(H)$ in terms of vertex degrees and we characterize the extremal hypergraphs attaining the bound, which solves a problem posed by Nikiforov [Analytic methods for uniform hypergraphs, Linear Algebra Appl. 457 (2014) 455–535]. Also, we prove a lower bound on $\rho(\mathcal{Q}(H))$ concerning degrees and give a characterization of the extremal hypergraphs attaining the bound.
DOI : 10.37236/6644
Classification : 05C50, 05C65, 15A18, 15A42
Mots-clés : uniform hypergraph, adjacency tensor, signless Laplacian tensor, spectral radius

Liying Kang  1   ; Lele Liu  1   ; Erfang Shan  1

1 Shanghai University 
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     author = {Liying Kang and Lele Liu and Erfang Shan},
     title = {Sharp lower bounds on the spectral radius of uniform hypergraphs concerning degrees},
     journal = {The electronic journal of combinatorics},
     year = {2018},
     volume = {25},
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     doi = {10.37236/6644},
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Liying Kang; Lele Liu; Erfang Shan. Sharp lower bounds on the spectral radius of uniform hypergraphs concerning degrees. The electronic journal of combinatorics, Tome 25 (2018) no. 2. doi: 10.37236/6644

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