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Digraphs with Hermitian spectral radius below 2 and their cospectrality with paths
- Source :
- Discrete Mathematics. 340:2616-2632
- Publication Year :
- 2017
- Publisher :
- Elsevier BV, 2017.
-
Abstract
- It is well-known that the paths are determined by the spectrum of the adjacency matrix. For digraphs, every digraph whose underlying graph is a tree is cospectral to its underlying graph with respect to the Hermitian adjacency matrix ( H -cospectral). Thus every (simple) digraph whose underlying graph is isomorphic to P n is H -cospectral to P n . Interestingly, there are others. This paper finds digraphs that are H -cospectral with the path graph P n and whose underlying graphs are nonisomorphic, when n is odd, and finds that such graphs do not exist when n is even. In order to prove this result, all digraphs whose Hermitian spectral radius is smaller than 2 are determined.
- Subjects :
- Discrete mathematics
Mathematics::Combinatorics
0211 other engineering and technologies
Voltage graph
021107 urban & regional planning
0102 computer and information sciences
02 engineering and technology
01 natural sciences
Distance-regular graph
Theoretical Computer Science
Combinatorics
Graph energy
Computer Science::Discrete Mathematics
010201 computation theory & mathematics
Graph power
Discrete Mathematics and Combinatorics
Regular graph
Adjacency matrix
Complement graph
Mathematics
Universal graph
Subjects
Details
- ISSN :
- 0012365X
- Volume :
- 340
- Database :
- OpenAIRE
- Journal :
- Discrete Mathematics
- Accession number :
- edsair.doi...........ce4c0c26d651739cae7de210eb3ef08e