Geodesic
On the α-Spectral Radius of Uniform Hypergraphs
Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 2, pp. 559-575

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For 0 ≤ α lt; 1 and a uniform hypergraph G, the α-spectral radius of G is the largest H-eigenvalue of α𝒟(G)+(1−α)𝒜(G), where 𝒟(G) and 𝒜(G) are the diagonal tensor of degrees and the adjacency tensor of G, respectively. We give upper bounds for the α-spectral radius of a uniform hypergraph, propose some transformations that increase the α-spectral radius, and determine the unique hypergraphs with maximum α-spectral radius in some classes of uniform hypergraphs.
Keywords: adjacency tensor, uniform hypergraph, extremal hypergraph, α-spectral radius, α-Perron vector 
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Guo, Haiyan; Zhou, Bo. On the α-Spectral Radius of Uniform Hypergraphs. Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 2, pp. 559-575. http://geodesic.mathdoc.fr/item/DMGT_2020_40_2_a11/