Spectra of transformation digraphs of a regular digraph. (English) Zbl 1207.05122
Summary: Let \(D = (V(D), A(D))\) be a digraph, \(x, y, z\) be three variables taking values \(-\) or \(+\), and \(D^{xyz}\) denote the transformation digraphs of \(D\). In this article, we determine the spectra of seven transformation digraphs of regular digraph \(D\) in terms of the spectrum of \(D\).
MSC:
05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
05C20 | Directed graphs (digraphs), tournaments |
05B20 | Combinatorial aspects of matrices (incidence, Hadamard, etc.) |
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