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.) |
References:
| [1] | Bondy JA, Graph Theory with Applications (1976) |
| [2] | DOI: 10.4153/CMB-1966-021-x · Zbl 0139.41601 · doi:10.4153/CMB-1966-021-x |
| [3] | Cvetkovic DM, Publ. Inst. Math. (Beograd) 16 pp 49– (1973) |
| [4] | Gantmacher FR, Theory of Matrices (1960) |
| [5] | DOI: 10.1090/S0002-9939-1965-0191841-6 · doi:10.1090/S0002-9939-1965-0191841-6 |
| [6] | DOI: 10.1017/CBO9780511626302 · Zbl 1106.37301 · doi:10.1017/CBO9780511626302 |
| [7] | Liu J, Ars Comb. 87 pp 97– (2008) |
| [8] | DOI: 10.1016/j.laa.2005.09.012 · Zbl 1083.05030 · doi:10.1016/j.laa.2005.09.012 |
| [9] | Wu B, J. Math. Study 34 pp 109– (2001) |
| [10] | DOI: 10.1016/j.disc.2005.04.002 · Zbl 1066.05095 · doi:10.1016/j.disc.2005.04.002 |
| [11] | Zhang F, J. Xinjiang Univ. (Nat. Sci. Ed.) 4 pp 1– (1987) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
