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Laplacian spectral characterization of roses
- Source :
- Linear Algebra and its Applications, 536, 19-30. Elsevier Inc.
- Publication Year :
- 2018
-
Abstract
- A rose graph is a graph consisting of cycles that all meet in one vertex. We show that except for two specific examples, these rose graphs are determined by the Laplacian spectrum, thus proving a conjecture posed by Lui and Huang [F.J. Liu and Q.X. Huang, Laplacian spectral characterization of 3-rose graphs, Linear Algebra Appl. 439 (2013), 2914--2920]. We also show that if two rose graphs have a so-called universal Laplacian matrix with the same spectrum, then they must be isomorphic. In memory of Horst Sachs (1927-2016), we show the specific case of the latter result for the adjacency matrix by using Sachs' theorem and a new result on the number of matchings in the disjoint union of paths.
- Subjects :
- Vertex (graph theory)
Closed walks
Matchings
010103 numerical & computational mathematics
0102 computer and information sciences
01 natural sciences
Combinatorics
Laplacian spectrum
Sachs' theorem
FOS: Mathematics
Discrete Mathematics and Combinatorics
Mathematics - Combinatorics
Adjacency matrix
0101 mathematics
Mathematics
Discrete mathematics
Numerical Analysis
Algebra and Number Theory
Conjecture
Graph
Rose graphs
010201 computation theory & mathematics
Geometry and Topology
Combinatorics (math.CO)
Laplacian matrix
05C50
Laplace operator
Subjects
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 536
- Database :
- OpenAIRE
- Journal :
- Linear Algebra and its Applications
- Accession number :
- edsair.doi.dedup.....fc3b5389b6529071d1d1180fdc3f1ab1