Abstract
In this paper, we characterize the extremal digraphs with the maximal or minimal α-spectral radius among some digraph classes such as rose digraphs, generalized theta digraphs and tri-ring digraphs with given size m. These digraph classes are denoted by , and (m) respectively. The main results about spectral extremal digraph by Guo and Liu [Some results on the spectral radius of generalized ∞ and θ-digraphs. Linear Algebra Appl. 2012;437(9):2200–2208] and Li et al. [The signless Laplacian spectral radius of some strongly connected digraphs. Indian J Pure Appl Math. 2018;49(1):113–127] are generalized to α-spectral graph theory. As a by-product of our main results, an open problem in Li et al. [The signless Laplacian spectral radius of some strongly connected digraphs. Indian J Pure Appl Math. 2018;49(1):113–127] is answered. Furthermore, we determine the digraphs with the first three minimal α-spectral radius among all strongly connected digraphs. Meanwhile, we determine the unique digraph with the fourth minimal α-spectral radius among all strongly connected digraphs for .
Disclosure statement
No potential conflict of interest was reported by the author(s).