Cospectrality Graphs of Smith Graphs
Апстракт
Graphs whose spectrum belongs to the interval [-2, 2] are called Smith graphs. The structure of a Smith graph with a given spectrum depends on a system of Diophantine linear algebraic equations. We have established in [1] several properties of this system and showed how it can be simplified and effectively applied. In this way a spectral theory of Smith graphs has been outlined. In the present paper we introduce cospectrality graphs for Smith graphs and study their properties through examples and theoretical consideration. The new notion is used in proving theorems on cospectrality of Smith graphs. In this way one can avoid the use of the mentioned system of Diophantine linear algebraic equations.
Кључне речи:
spectral radius / spectral graph theory / Smith graphs / Diophantine equations / cospectrality graphsИзвор:
Filomat, 2019, 33, 11, 3269-3276Издавач:
- Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
Финансирање / пројекти:
- Теорија графова и математичко програмирање са применама у хемији и рачунарству (RS-MESTD-Basic Research (BR or ON)-174033)
- Методе функционалне и хармонијске анализе и ПДЈ са сингуларитетима (RS-MESTD-Basic Research (BR or ON)-174024)
DOI: 10.2298/FIL1911269C
ISSN: 0354-5180
WoS: 000500749700001
Scopus: 2-s2.0-85077899879
Институција/група
Fakultet organizacionih naukaTY - JOUR AU - Cvetković, Dragoš AU - Todorčević, Vesna PY - 2019 UR - https://rfos.fon.bg.ac.rs/handle/123456789/1928 AB - Graphs whose spectrum belongs to the interval [-2, 2] are called Smith graphs. The structure of a Smith graph with a given spectrum depends on a system of Diophantine linear algebraic equations. We have established in [1] several properties of this system and showed how it can be simplified and effectively applied. In this way a spectral theory of Smith graphs has been outlined. In the present paper we introduce cospectrality graphs for Smith graphs and study their properties through examples and theoretical consideration. The new notion is used in proving theorems on cospectrality of Smith graphs. In this way one can avoid the use of the mentioned system of Diophantine linear algebraic equations. PB - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš T2 - Filomat T1 - Cospectrality Graphs of Smith Graphs EP - 3276 IS - 11 SP - 3269 VL - 33 DO - 10.2298/FIL1911269C UR - conv_2242 ER -
@article{ author = "Cvetković, Dragoš and Todorčević, Vesna", year = "2019", abstract = "Graphs whose spectrum belongs to the interval [-2, 2] are called Smith graphs. The structure of a Smith graph with a given spectrum depends on a system of Diophantine linear algebraic equations. We have established in [1] several properties of this system and showed how it can be simplified and effectively applied. In this way a spectral theory of Smith graphs has been outlined. In the present paper we introduce cospectrality graphs for Smith graphs and study their properties through examples and theoretical consideration. The new notion is used in proving theorems on cospectrality of Smith graphs. In this way one can avoid the use of the mentioned system of Diophantine linear algebraic equations.", publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš", journal = "Filomat", title = "Cospectrality Graphs of Smith Graphs", pages = "3276-3269", number = "11", volume = "33", doi = "10.2298/FIL1911269C", url = "conv_2242" }
Cvetković, D.,& Todorčević, V.. (2019). Cospectrality Graphs of Smith Graphs. in Filomat Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 33(11), 3269-3276. https://doi.org/10.2298/FIL1911269C conv_2242
Cvetković D, Todorčević V. Cospectrality Graphs of Smith Graphs. in Filomat. 2019;33(11):3269-3276. doi:10.2298/FIL1911269C conv_2242 .
Cvetković, Dragoš, Todorčević, Vesna, "Cospectrality Graphs of Smith Graphs" in Filomat, 33, no. 11 (2019):3269-3276, https://doi.org/10.2298/FIL1911269C ., conv_2242 .
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