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.
Keywords:
Graph eigenvalue / Tree / Double star / Acyclic matrix / Star complement
Source:
Filomat, 2013, 27, 8, 1455-1461
Publisher:
Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
TY - JOUR
AU - Erić, Aleksandra
AU - da Fonseca, C. M.
PY - 2013
UR - https://grafar.grf.bg.ac.rs/handle/123456789/492
AB - 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.
PB - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
T2 - Filomat
T1 - Some consequences of an inequality on the spectral multiplicity of graphs
EP - 1461
IS - 8
SP - 1455
VL - 27
DO - 10.2298/FIL1308455E
ER -
@article{
author = "Erić, Aleksandra and da Fonseca, C. M.",
year = "2013",
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.",
publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš",
journal = "Filomat",
title = "Some consequences of an inequality on the spectral multiplicity of graphs",
pages = "1461-1455",
number = "8",
volume = "27",
doi = "10.2298/FIL1308455E"
}
Erić, A.,& da Fonseca, C. M.. (2013). Some consequences of an inequality on the spectral multiplicity of graphs. in Filomat
Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 27(8), 1455-1461.
https://doi.org/10.2298/FIL1308455E
Erić A, da Fonseca CM. Some consequences of an inequality on the spectral multiplicity of graphs. in Filomat. 2013;27(8):1455-1461.
doi:10.2298/FIL1308455E .
Erić, Aleksandra, da Fonseca, C. M., "Some consequences of an inequality on the spectral multiplicity of graphs" in Filomat, 27, no. 8 (2013):1455-1461,
https://doi.org/10.2298/FIL1308455E . .
