Some consequences of an inequality on the spectral multiplicity of graphs
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.
Keywords:
Graph eigenvalue / Tree / Double star / Acyclic matrix / Star complementSource:
Filomat, 2013, 27, 8, 1455-1461Publisher:
- Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
DOI: 10.2298/FIL1308455E
ISSN: 0354-5180
WoS: 000329319100009
Scopus: 2-s2.0-84888402108
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Institution/Community
GraFarTY - 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 . .