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Eigenvalue multiplicity of a graph in terms of the number of external vertices.
- Source :
-
Linear Algebra & its Applications . Aug2024, Vol. 694, p18-29. 12p. - Publication Year :
- 2024
-
Abstract
- The multiplicity of an eigenvalue λ of a graph G is denoted by m (G , λ). In a connected graph G with at least two vertices, a vertex is called external if it is not a cut vertex. In a tree, an external vertex is exactly a pendant vertex. Let ϵ (G) be the number of external vertices in G. In this paper, we prove that m (G , λ) ≤ ϵ (G) − 1 for any λ and characterize the extremal graphs with m (G , − 1) = ϵ (G) − 1 , which generalizes the main result of Wang et al. [Linear Multi. Alg., 2020] from a tree to an arbitrary connected graph. [ABSTRACT FROM AUTHOR]
- Subjects :
- *EIGENVALUES
*MULTIPLICITY (Mathematics)
*GRAPH connectivity
*REGULAR graphs
Subjects
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 694
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 177289638
- Full Text :
- https://doi.org/10.1016/j.laa.2024.04.009