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

Let G be a k -uniform hypergraph with vertex set V (G) and edge set E (G). A connected and acyclic hypergraph is called a supertree. For 0 ≤ α < 1 , the α -spectral radius of G is the largest H -eigenvalue of α D (G) + (1 − α) A (G) , where D (G) and A (G) are the diagonal tensor of the degrees and the adjacency tensor of G , respectively. In this paper, we determine the unique supertrees with maximum α -spectral radius among all k -uniform supertrees with m edges and independence number β for ⌈ m (k − 1) + 1 k ⌉ ≤ β ≤ m , among all k -uniform supertrees with given degree sequences, and among all k -uniform supertrees with m edges and matching number μ for 1 ≤ μ ≤ ⌊ m (k − 1) + 1 k ⌋ , respectively. [ABSTRACT FROM AUTHOR]