The maximum spectral radii of uniform supertrees with given degree sequences

“…The spectral radii of k-uniform supertrees have been studied by many authors (see [3,13,14]). In [15,16], Yuan et al determined the top ten supertrees with the maximum spectral radii. And in [4], Guo et al determined the unique non-hyper-caterpillar with maximum adjacency spectral radius among N C(m, d).…”

Section: Introductionmentioning

confidence: 99%

On some properties of the α-spectral radius of the k-uniform hypergraph

Wang

Shan

Wang

2020

Linear Algebra and its Applications

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“…In 1987, Stanley [18] proved that the spectral radius of a graph G with e edges is at most On the problem of maximizing spectral radius of a certain class of hypergraphs, Fan, Tan, Peng and Liu [6] determined the extremal spectral radii of several classes of r-uniform hypergraphs with few edges. Xiao, Wang and Lu [19] determined the unique r-uniform supertrees with maximum spectral radii among all r-uniform supertrees with given degree sequences. Li, Shao, and Qi [13] determined the extremal spectral radii of r-uniform supertrees.…”

Section: Historymentioning

confidence: 99%

A bound on the spectral radius of hypergraphs with e edges

Bai

Lü

2018

Linear Algebra and its Applications

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For r ≥ 3, let fr : [0, ∞) → [1, ∞) be the unique analytic function such that fr( k r ) = k−1 r−1 for any k ≥ r − 1. We prove that the spectral radius of an r-uniform hypergraph H with e edges is at most fr(e). The equality holds if and only if e = k r for some positive integer k and H is the union of a complete r-uniform hypergraph K r k and some possible isolated vertices. This result generalizes the classical Stanley's theorem on graphs. √ 1+8e−1 2. The equality holds if and only if e = k 2 and G is the union of the complete graph K k and some isolated vertices. Friedland [7] proved a bound which is tight on the complete graph with one, two, or three edges removed or the complete graph with one edge added. Rowlinson [17] finally confirmed Brualdi and Hoffman's conjecture, and proved that G e attains the maximum spectral radius among all graphs with e edges.

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“…Fan et al [3] determined the hypergraphs with maximum spectral radius among uniform hypergraphs with few edges. Xiao et al [15] determined the hypertree with maximum spectral radius among uniform hypertrees with a given degree sequence. See [] for more work on hypergraphs with maximum spectral radius in someclasses of uniform hypergraphs.…”

Section: Introductionmentioning

confidence: 99%