TY  - CONF
AU  - Cvetković, Dragoš
AU  - Dražić, Zorica
AU  - Kovačević-Vujčić, Vera
AU  - Čangalović, Mirjana
PY  - 2018
UR  - https://dais.sanu.ac.rs/123456789/9081
AB  - We consider the symmetric traveling salesman problem (TSP) with instances represented by complete graphs with distances between cities as edge weights. Computational experiments with randomly generated instances on 50 and 100 vertices with the
uniform distribution of integer edge weights in interval [1, 100] show that there exists a correlation between the sequences of the spectral radii of the distance matrices and the lengths
of optimal tours obtained by the well known TSP solver Concorde. In this paper we give a
partial theoretical explanation of this correlation.
PB  - Beograd : Académie Serbe des sciences et des arts
C3  - Bulletin T.CLI de l’Académie serbe des sciences et des arts
T1  - The traveling salesman problem: The spectral radius and the length of an optimal tour
SP  - 17
EP  - 26
UR  - https://hdl.handle.net/21.15107/rcub_dais_9081
ER  - 

@conference{
author = "Cvetković, Dragoš and Dražić, Zorica and Kovačević-Vujčić, Vera and Čangalović, Mirjana",
year = "2018",
abstract = "We consider the symmetric traveling salesman problem (TSP) with instances represented by complete graphs with distances between cities as edge weights. Computational experiments with randomly generated instances on 50 and 100 vertices with the
uniform distribution of integer edge weights in interval [1, 100] show that there exists a correlation between the sequences of the spectral radii of the distance matrices and the lengths
of optimal tours obtained by the well known TSP solver Concorde. In this paper we give a
partial theoretical explanation of this correlation.",
publisher = "Beograd : Académie Serbe des sciences et des arts",
journal = "Bulletin T.CLI de l’Académie serbe des sciences et des arts",
title = "The traveling salesman problem: The spectral radius and the length of an optimal tour",
pages = "17-26",
url = "https://hdl.handle.net/21.15107/rcub_dais_9081"
}

Cvetković, D., Dražić, Z., Kovačević-Vujčić, V.,& Čangalović, M.. (2018). The traveling salesman problem: The spectral radius and the length of an optimal tour. in Bulletin T.CLI de l’Académie serbe des sciences et des arts
Beograd : Académie Serbe des sciences et des arts., 17-26.
https://hdl.handle.net/21.15107/rcub_dais_9081

Cvetković D, Dražić Z, Kovačević-Vujčić V, Čangalović M. The traveling salesman problem: The spectral radius and the length of an optimal tour. in Bulletin T.CLI de l’Académie serbe des sciences et des arts. 2018;:17-26.
https://hdl.handle.net/21.15107/rcub_dais_9081 .

Cvetković, Dragoš, Dražić, Zorica, Kovačević-Vujčić, Vera, Čangalović, Mirjana, "The traveling salesman problem: The spectral radius and the length of an optimal tour" in Bulletin T.CLI de l’Académie serbe des sciences et des arts (2018):17-26,
https://hdl.handle.net/21.15107/rcub_dais_9081 .

TY  - JOUR
AU  - Cvetković, Dragoš
PY  - 2017
UR  - https://dais.sanu.ac.rs/123456789/16441
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 Diofantine
linear algebraic equations. We establish several properties of this system and show
how it can be simplified and effectively applied.
PB  - Beograd : Académie Serbe des sciences et des arts
T2  - Bulletin T.CL de l’Académie serbe des sciences et des arts
T1  - Spectral theory of Smith graphs
SP  - 19
EP  - 40
UR  - https://hdl.handle.net/21.15107/rcub_dais_16441
ER  - 

@article{
author = "Cvetković, Dragoš",
year = "2017",
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 Diofantine
linear algebraic equations. We establish several properties of this system and show
how it can be simplified and effectively applied.",
publisher = "Beograd : Académie Serbe des sciences et des arts",
journal = "Bulletin T.CL de l’Académie serbe des sciences et des arts",
title = "Spectral theory of Smith graphs",
pages = "19-40",
url = "https://hdl.handle.net/21.15107/rcub_dais_16441"
}

Cvetković, D.. (2017). Spectral theory of Smith graphs. in Bulletin T.CL de l’Académie serbe des sciences et des arts
Beograd : Académie Serbe des sciences et des arts., 19-40.
https://hdl.handle.net/21.15107/rcub_dais_16441

Cvetković D. Spectral theory of Smith graphs. in Bulletin T.CL de l’Académie serbe des sciences et des arts. 2017;:19-40.
https://hdl.handle.net/21.15107/rcub_dais_16441 .

Cvetković, Dragoš, "Spectral theory of Smith graphs" in Bulletin T.CL de l’Académie serbe des sciences et des arts (2017):19-40,
https://hdl.handle.net/21.15107/rcub_dais_16441 .

TY  - JOUR
AU  - Cvetković, Dragoš
AU  - Davidović, Tatjana
AU  - Jovanović, Irena M.
PY  - 2016
UR  - https://dais.sanu.ac.rs/123456789/947
AB  - A multiprocessor system can be modeled by a graph G. The vertices of G correspond to processors while edges represent links between processors. To find suitable models for multiprocessor interconnection networks (briefly MINs), one can apply tools and techniques of spectral graph theory. In this paper, we extend some of the existing results and present several graphs which could serve as models for e cient MINs based on the small values of the previously introduced graph tightness. These examples of possible MINs arise as a result of some well-known and widely used graph operations. We also examine the suitability of strongly regular graphs (briefly SRGs) to model MINs, and prove the uniqueness of some of them.
T2  - Yugoslav Journal of Operations Research
T1  - Some new models for multiprocessor interconnection networks
SP  - 423
EP  - 439
VL  - 26
IS  - 4
DO  - 10.2298/YJOR160315020C
UR  - https://hdl.handle.net/21.15107/rcub_dais_947
ER  - 

@article{
author = "Cvetković, Dragoš and Davidović, Tatjana and Jovanović, Irena M.",
year = "2016",
abstract = "A multiprocessor system can be modeled by a graph G. The vertices of G correspond to processors while edges represent links between processors. To find suitable models for multiprocessor interconnection networks (briefly MINs), one can apply tools and techniques of spectral graph theory. In this paper, we extend some of the existing results and present several graphs which could serve as models for e cient MINs based on the small values of the previously introduced graph tightness. These examples of possible MINs arise as a result of some well-known and widely used graph operations. We also examine the suitability of strongly regular graphs (briefly SRGs) to model MINs, and prove the uniqueness of some of them.",
journal = "Yugoslav Journal of Operations Research",
title = "Some new models for multiprocessor interconnection networks",
pages = "423-439",
volume = "26",
number = "4",
doi = "10.2298/YJOR160315020C",
url = "https://hdl.handle.net/21.15107/rcub_dais_947"
}

Cvetković, D., Davidović, T.,& Jovanović, I. M.. (2016). Some new models for multiprocessor interconnection networks. in Yugoslav Journal of Operations Research, 26(4), 423-439.
https://doi.org/10.2298/YJOR160315020C
https://hdl.handle.net/21.15107/rcub_dais_947

Cvetković D, Davidović T, Jovanović IM. Some new models for multiprocessor interconnection networks. in Yugoslav Journal of Operations Research. 2016;26(4):423-439.
doi:10.2298/YJOR160315020C
https://hdl.handle.net/21.15107/rcub_dais_947 .

Cvetković, Dragoš, Davidović, Tatjana, Jovanović, Irena M., "Some new models for multiprocessor interconnection networks" in Yugoslav Journal of Operations Research, 26, no. 4 (2016):423-439,
https://doi.org/10.2298/YJOR160315020C .,
https://hdl.handle.net/21.15107/rcub_dais_947 .