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

Sharp Bounds on the Spectral Radii of Uniform Hypergraphs concerning Diameter or Clique Number

“…Lemma 7 (see [17]). Let u, v be two non-pendant vertices of hypergraph H. If there exist an internal path P with s length in hypergraph H p,q (u, v) for any p ≥ q ≥ 1, then we have…”

“…Xiao et al [9] determined the supertrees with the first two largest spectral radii among all supertrees in the set of m-uniform supertrees with r edges and diameter d. Su et al [10] determined the first ⌊d/2⌋ + 1 largest spectral radius of k-uniform supertrees with size m and diameter d. In addition, the first two smallest spectral radii of supertrees with size m are also determined. For other related results, readers are referred to [11][12][13][14][15][16][17][18][19][20]. In the spirit of the general problem of Brualdi and Solheid [21], one can ask how large or how small can be the spectral radius of hypergraphs with some specific properties.…”

The smallest spectral radius of bicyclic uniform hypergraphs with a given size

“…In this section, we study the effects on spectral radii of k-graphs under the operations:vertex-splitting and vertex-releasing operations. Definition 4.1 (Edge moving operation [16]). For k ≥ 2, let G be a k-uniform hypergraph with u, v 1 , .…”

On the $α$-spectral radius of the $k$-uniform supertrees

“…Guo and Zhou [4] introduced some transformations which increase the α-spectral radius, and determined the unique hypergraph with the largest α-spectral radius in some classes of uniform hypergraphs. Wang et al [17] showed how the α-spectral changes under the edge grafting operations on connected k-uniform hypergraphs, and obtained the extremal supertree for α-spectral radius among k-uniform non-caterpillar hypergraphs with given order, size and diameter. In 2022, Kang et al [6] determined the unique unicyclic hypergraphs with the maximum α-spectral radius among all k-uniform unicyclic hypergraphs with fixed diameter, and among all k-uniform unicyclic hypergraphs with given number of pendent edges.…”