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On weight-symmetric 3-coloured digraphs.
- Source :
-
Linear & Multilinear Algebra . 2023, Vol. 71 Issue 17, p2744-2762. 19p. - Publication Year :
- 2023
-
Abstract
- We consider particular weighted directed graphs with edges having colour red, blue or green such that each red edge has weight 1, each blue edge has weight $ -1 $ − 1 and each green edge has weight $ \mathrm {i} $ i (the imaginary unit). Such a directed graph is called a 3-coloured digraph (for short, a 3-CD). Every mixed graph and every signed graph can be interpreted as a 3-CD. We first study some structural properties of 3-CDs by means of the eigenvalues of the adjacency matrix. In particular, we give spectral criteria for singularity of such digraphs. Second, we consider weight-symmetric 3-CDs, i.e. those 3-CDs that are switching isomorphic to their negation. It follows that the class of weight-symmetric 3-CDs is included in the class of 3-CDs whose spectrum is symmetric (with respect to the origin). We give some basic properties and several constructions of weight-symmetric 3-CDs and establish constructions of 3-CDs which have symmetric spectrum but are not weight-symmetric. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DIRECTED graphs
*WEIGHTED graphs
*EIGENVALUES
Subjects
Details
- Language :
- English
- ISSN :
- 03081087
- Volume :
- 71
- Issue :
- 17
- Database :
- Academic Search Index
- Journal :
- Linear & Multilinear Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 174084098
- Full Text :
- https://doi.org/10.1080/03081087.2022.2119926