2013/04/04 by Shenglong Hu, Liqun Qi, Hu, Shenglong +3
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Spectral Theory (math.SP) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1304.1315
openalex publication_date 2013/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we show that the largest Laplacian H-eigenvalue of a k-uniform nontrivial hypergraph is strictly larger than the maximum degree when k is even. A tight lower bound for this eigenvalue is given. For a connected even-uniform hypergraph, this lower bound is achieved if and only if it is a hyperstar. However, when k is odd, it happens that the largest Laplacian H-eigenvalue is equal to the maximum degree, which is a tight lower bound. On the other hand, tight upper and lower bounds for the largest signless Laplacian H-eigenvalue of a k-uniform connected hypergraph are given. For a connected k-uniform hypergraph, the upper (respectively lower) bound of the largest signless Laplacian H-eigenvalue is achieved if and only if it is a complete hypergraph (respectively a hyperstar). The largest Laplacian H-eigenvalue is always less than or equal to the largest signless Laplacian H-eigenvalue. When the hypergraph is connected, the equality holds here if and only if k is even and the hypergraph is odd-bipartite.