Some α-spectral extremal results for some digraphs [article]

Haiying Shan, Feifei Wang, Changxiang He
2021 arXiv   pre-print
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 ℛ_m^k, Θ_k(m) and (m) respectively. The main results about spectral extremal digraph by Guo and Liu in and Li and Wang in are generalized to α-spectral graph theory. As a by-product of our main results, an open problem in is answered.
more » ... , 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 0≤α≤1/2.
arXiv:2105.03077v1 fatcat:tn6r4jmtkvdtjlow3vyqz3r5xy