On the spectra and energy of the A¥á matrix of digraphs

Let D be a digraph of order n with adjacency matrix A(D).For α ∈ [0, 1], the Aα-matrix of digraph D is defined aswhere z1, z2, . . ., zn are the eigenvalues of Aα(D), and Re(zi) denotes the real part of zi.In this paper, we determine the Aα-spectrum for several classes of digraphs.We also compute the Aα-energy for directed paths, directed cycles, bipartite digraphs, and k-regular digraphs.As a consequence, we obtain McClelland's inequality for the Aα-energy of k-regular digraphs.

Abstract licence: CC BY

3 more references, whose wording the paper’s licence keeps private.

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.