Some consequences of an inequality on the spectral multiplicity of graphs
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Abstract. We present two distinct applications of an inequality relating the multiplicity of an eigenvalue of
a graph to a certain subgraph. The first is related to a recent classification, established by Kim and Shader,
for the class of those trees for which each of the associated matrices have distinct eigenvalues whenever
the diagonal entries are distinct. We analyze the minimum number of distinct diagonal entries and the
corresponding location, in order to preserve such multiplicity characterization. The second application
involves a new property of a star set of a graph due to P. Rowlinson.
Кључне речи:
Graph eigenvalue / Tree / Double star / Acyclic matrix / Star complementИзвор:
Filomat, 2013, 27(8)1455-1461Финансирање / пројекти:
- EDUCIRC2022 - Circular economy as a model of development that forms a new identity of the Republic of Serbia (RS-ScienceFundRS-Identiteti-303)
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GraFarTY - JOUR AU - Erić, Aleksandra Lj. AU - da Fonseca, Carlos PY - 2013 UR - https://grafar.grf.bg.ac.rs/handle/123456789/3173 AB - Abstract. We present two distinct applications of an inequality relating the multiplicity of an eigenvalue of a graph to a certain subgraph. The first is related to a recent classification, established by Kim and Shader, for the class of those trees for which each of the associated matrices have distinct eigenvalues whenever the diagonal entries are distinct. We analyze the minimum number of distinct diagonal entries and the corresponding location, in order to preserve such multiplicity characterization. The second application involves a new property of a star set of a graph due to P. Rowlinson. T2 - Filomat T1 - Some consequences of an inequality on the spectral multiplicity of graphs VL - 27(8)1455-1461 DO - 10.2298/FILI308455E ER -
@article{ author = "Erić, Aleksandra Lj. and da Fonseca, Carlos", year = "2013", abstract = "Abstract. We present two distinct applications of an inequality relating the multiplicity of an eigenvalue of a graph to a certain subgraph. The first is related to a recent classification, established by Kim and Shader, for the class of those trees for which each of the associated matrices have distinct eigenvalues whenever the diagonal entries are distinct. We analyze the minimum number of distinct diagonal entries and the corresponding location, in order to preserve such multiplicity characterization. The second application involves a new property of a star set of a graph due to P. Rowlinson.", journal = "Filomat", title = "Some consequences of an inequality on the spectral multiplicity of graphs", volume = "27(8)1455-1461", doi = "10.2298/FILI308455E" }
Erić, A. Lj.,& da Fonseca, C.. (2013). Some consequences of an inequality on the spectral multiplicity of graphs. in Filomat, 27(8)1455-1461. https://doi.org/10.2298/FILI308455E
Erić AL, da Fonseca C. Some consequences of an inequality on the spectral multiplicity of graphs. in Filomat. 2013;27(8)1455-1461. doi:10.2298/FILI308455E .
Erić, Aleksandra Lj., da Fonseca, Carlos, "Some consequences of an inequality on the spectral multiplicity of graphs" in Filomat, 27(8)1455-1461 (2013), https://doi.org/10.2298/FILI308455E . .