ORIGINAL_ARTICLE
Connected and Hyperconnected Generalized Topological Spaces
A. Csaszar introduced and extensively studied the notion of generalized opensets. Following Csazar, we introduce a new notion hyperconnected. We study some specicproperties about connected and hyperconnected in generalized topological spaces. Finally, wecharacterize the connected component in generalized topological spaces.
http://jlta.iauctb.ac.ir/article_525272_3effe31d647d8985ed42836bc5a24d20.pdf
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229
234
Generalized topology
m-structure
weak structure
connected
g-closed
R
Messaoud
rimessaoud@yahoo.fr
true
1
university of Gafsa Tunisia
university of Gafsa Tunisia
university of Gafsa Tunisia
LEAD_AUTHOR
I
basdouri
basdourimd@yahoo.fr
true
2
university of Gafsa Tunisia.
university of Gafsa Tunisia.
university of Gafsa Tunisia.
AUTHOR
A
Missaoui
amiramissaoui@yahoo.fr
true
3
university of Gafsa Tunisia
university of Gafsa Tunisia
university of Gafsa Tunisia
AUTHOR
[1] E. Bouacida, O. Echi, E. Salhi, Topologies associees a une relation binaire et relation binaire spectrale.
1
Bollettino della Unione Mathematica Italiana (7), 10-B (1996), 417-439.
2
[2] E. Bouassida, B. Ghanmi, R. Messaoud, A. Missaoui, Generalized superconnectedness, Journal of Linear and
3
Topological Algebra, 04 (04) (2015), 267-273.
4
[3] E. CECH, Topologicke prostory. Cas. pest, mat., 66 (1936-37), 225-264.
5
[4] A. Csazar, Generalized topology, generalized continuity, Acta math. Hungar., 96 (2002), 351-357.
6
[5] A. Csazar, Generalized open sets in generalized topologies, Acta math. Hungar., 106 (2005), 53-66.
7
[6] A. Csazar, Grundlagen der allgemeinen Topologie. Budapest 1963.
8
[7] A. Csazar, Weak structres, Acta math. Hungar 131 (1-2) (2011), 193-195.
9
[8] A. Csazar, -connected sets, Acta Math. Hungar. 101 (2003), 273-279.
10
[9] A. Csazar, Normal generalized topologies, Acta Math. Hungar. 115 (4) (2007), 309-313.
11
[10] A. Csazar, and -modications of generalized topologies, Acta Math. Hungar. 120 (2008), 275-279.
12
[11] F. Hausdor, Gestufte Raume. Fundamenta mathematicae, 25 (1935), 486-502.
13
[12] J. L. Kelley, General Topology. D. Van Nostrand company, New York 1955.
14
[13] W. K. Min, Generalized continuous functions dened by generalized open sets on generalized topological
15
spaces, Acta Math. Hungar., 128 (2009), doi: 10.1007/s10474-009-9037-6.
16
[14] D. Jayanthi, Contra Continuity on generalized topological spaces, Acta Math. Hungar., 137 (4) (2012), 263-
17
ORIGINAL_ARTICLE
On quasi-baer modules
Let R be a ring, be an endomorphism of R and MR be a -rigid module. Amodule MR is called quasi-Baer if the right annihilator of a principal submodule of R isgenerated by an idempotent. It is shown that an R-module MR is a quasi-Baer module if andonly if M[[x]] is a quasi-Baer module over the skew power series ring R[[x; ]].
http://jlta.iauctb.ac.ir/article_523166_7c8fd553c55afdb046ff1bc23fb771ff.pdf
2016-12-01T11:23:20
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235
240
Quasi-Baer modules
-rigid modules
quasi-Armendariz modules
M
Shafiee-Mousavi
mshafieemousavi@azad.ac.ir
true
1
Islamic Azad University, South Tehran Branch
Islamic Azad University, South Tehran Branch
Islamic Azad University, South Tehran Branch
LEAD_AUTHOR
[1] D. D. Anderon, V. Camilo, Armendariz rings and gaussian rings. Comm. Algebra 26 (1998) 2265-2275.
1
[2] S. Aninn, Associated primes over skew polynomials rings. Comm. Algebra 30 (2002) 2511-2528.
2
[3] E. P. Armendariz, A note on extensions of Baer and p.p.rings. J. Austral. Math. Soc. 18 (1974) 470-473.
3
[4] G. F. Birkenmeier, J. Y. Kim, J. K. Park, On quasi-Baer rings. Algebra and it applications (Athens, OH)
4
(1999) 67-92.
5
[5] G. F. Birkenmeier, J. Y. Kim, J. K. Park, Principally quasi-Baer rings. Comm. Algebra 29 (2011) 639-660.
6
[6] G. F. Birkenmeier, J. Y. Kim, J. K. Park, Polynomial extensions of Baer and quasi-Baer rings. J. Pure Appl.
7
Algebra 159 (2001) 25-42.
8
[7] G. F. Birkenmeier, Idempotents and completely semiprime ideals. Comm. Algebra. 11 (1983) 567-580.
9
[8] J. W. Brewer, Power series over commutative rings. Lecture Notes in Pure and Applied Mathematics, 64,
10
Marcel Dekker, Inc., New York 1981.
11
[9] A. W. Chatters, C. R. Hajarnavis, Rings with chain conditions. Research Nots in Mathematics. 44, Pitman,
12
Boston, Mas.-London, 1980.
13
[10] W. E. Clark, Twited matrix units semigroup algebras. Duke Math. J. 34 (1967) 417-424
14
[11] E. Hashemi, A. Moussavi, Polynomial extensions of quasi-Baer rings. Acta Math. Hungar. 107 (2005) 207-224.
15
[12] Y. Hirano, On annihilator ideals of a polynomial ring over a non commutative ring. J. Pure Appl. Algebra.
16
168 (2002) 45-52.
17
[13] C. Y. Hong. N. K. Kim, T. K. Kwak, On skew Armendariz rings. Comm. Algebra. 31 (2003) 103-122.
18
[14] C. Huh, Y. Lee, Smoktunowicz, Agata, Armendariz rings and semicommutativ rings. Comm. Algebra. 30
19
(2002) 751-761.
20
[15] I. Kaplansky, Rings of operators. W. A. Benjamin, Inc., New York, 1968.
21
[16] N. K. Kim, K. H. Lee, Y. Lee, Power eris rings satisfying a zero divisor property. Comm. Algebra. 34 (2006)
22
2205-2218.
23
[17] N. K. Kim, Y. Lee, Armendariz rings and reduced rings. J. Algebra 223 (2000) 447-488.
24
[18] J. Krempa, Some examples of reduced rings. Algebra Colloq. 3 (1996) 289-300.
25
[19] T. K. Lee, Y. Zhou, Armendariz and reduced rings. Comm. Algebra. 32 (2004) 2287-2299.
26
[20] T. K. Lee, Y. Zhou, Reduced modules. Rings, modules, algebras and abelian groups. 365-377. Lecture Notes
27
in Pure and Appl. Math., 236. Marcel Dekker, New York, 2004.
28
[21] Z. Liu, A note on principally quai-Baer rings. Comm. Algebra. 30 (2002) 3885-3890.
29
[22] M. B. Rege, S. Chhawchharia, Armendariz rings. Proc. Japan Acad. Ser. A Math. Sci. 73 (1997) 14-17.
30
[23] L. Zhongkui, Z. Renyu, A generalization of p.p.-rings and p.q.-Baer rings. Glasgow Math. J. 48 (2006) 217-229.
31
ORIGINAL_ARTICLE
Construction of strict Lyapunov function for nonlinear parameterised perturbed systems
In this paper, global uniform exponential stability of perturbed dynamical systemsis studied by using Lyapunov techniques. The system presents a perturbation term which isbounded by an integrable function with the assumption that the nominal system is globallyuniformly exponentially stable. Some examples in dimensional two are given to illustrate theapplicability of the main results.
http://jlta.iauctb.ac.ir/article_524186_3d72c602686e0c948dbea988d6efc016.pdf
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241
261
Perturbed systems
Lyapunov function
uniform exponential stability
B
Ghanmi
boulbaba_ghanmi@yahoo.fr
true
1
Faculty of science, University of Sfax, Sfax, Tunisia.
Faculty of science, University of Sfax, Sfax, Tunisia.
Faculty of science, University of Sfax, Sfax, Tunisia.
LEAD_AUTHOR
M. A.
Hammami
true
2
Faculty of science, University of Sfax, Sfax, Tunisia
Faculty of science, University of Sfax, Sfax, Tunisia
Faculty of science, University of Sfax, Sfax, Tunisia
AUTHOR
[1] A. Benabdallah, M. Dlala and M. A. Hammami, A new Lyapunov function for stability of time-varying
1
nonlinear perturbed systems. Systems and Control Letters, 56 (2007) 179-187.
2
[2] F. Camilli, L. Grne, F. Wirth, Zubovs method for perturbed dierential equations, in: Proceedings of the
3
Mathematical Theory of Networks and Systems, Perpignan, 2000, CD-ROM, article B100.
4
[3] F. Camilli, L. Grne, F. Wirth, A generalization of Zubovs method to perturbed systems. SIAM J. Control
5
Optim. 40 (2001) 496-515.
6
[4] S. Dubljevic, N. Kazantzis, A new Lyapunov design approach for nonlinear systems based on Zubovs method.
7
Automatica 38 (2002), 1999-2007.
8
[5] W. Hahn, Stability of Motion. Springer, Berlin, Heidelberg, 1967.
9
[6] M. A. Hammami, On the stability of nonlinear control systems with uncertainty. J. Dynamical Control
10
Systems 7 (2) (2001), 171-179.
11
[7] H. K. Khalil, Nonlinear Systems. third ed., Prentice-Hall, Englewood Clis, NJ, 2002.
12
[8] V. Lakshmikantham, S. Leela an A.A. Matynuk, Practical stability of nonlinear systems. World scientic
13
Publishing Co. Pte. Ltd. 1990.
14
[9] Y. Lin, E. Sontag, Y. Wang, A smooth converse Lyapunov theorem for robust stability. SIAM J. Control
15
Optim. 34 (1) (1996), 124-160.
16
[10] A. A. Martynuk, Stability in the models of real world phenomena. Nonlinear Dyn. Sys. Theory 11 (1) (2011),
17
[11] F. Mazenc. Strict Lyapunov Fonctions for Time-varying Systems. Automatica 39 (2003), 349-353.
18
[12] D. R. Merkin, Introduction to the Theory of Stability. Springer, New York, Berlin, Heidelberg, 1996.
19
[13] E. Panteley, A. Loria, Global uniform asymptotic stability of cascaded nonautonomous nonlinear systems, in:
20
Proceedings of the Fourth European Control Conference, Louvain-La-Neuve, Belgium, Julis, paper no. 259,
21
[14] E. Panteley, A. Loria, Growth rate conditions for uniform asymptotic stability of cascaded time-varying
22
systems. Automatica 37 (2001) 453-460.
23
[15] V.N. Phat, Global stabilization for linear continuous time-varing systems. Applied Mathematics and Com-
24
putation 175 (2006), 1730-1743.
25
[16] N. Rouche, P. Habets, M. Laloy, Stability theory by Lyapunovs direct method. Appl. Math. Sci. 22 (1977).
26
[17] R. Sepulchre, M. Jankovic, P.V. Kokotovic, Constructive Lyapunov stabilization of nonlinear cascade systems.
27
IEEE Trans. Automat. Control 41 (12) (1996), 1723-1735.
28
ORIGINAL_ARTICLE
On the irreducibility of the complex specialization of the representation of the Hecke algebra of the complex re ection group G7
We consider a 2-dimensional representation of the Hecke algebra H(G7; u), whereG7 is the complex re ection group and u is the set of indeterminatesu = (x1; x2; y1; y2; y3; z1; z2; z3):After specializing the indetrminates to non zero complex numbers, we then determine a nec-essary and sucient condition that guarantees the irreducibility of the complex specializationof the representation of the Hecke algebra H(G7; u).
http://jlta.iauctb.ac.ir/article_525145_c823f0b9a87e816b0e0d7866259cf663.pdf
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263
270
Braid group
Hecke algebra
irreducible
re ections
M. Y
Chreif
myc102@student.bau.edu.lb
true
1
Department of Matehmatics
Faculty of Science
Beirut Arab University
Beirut, Lebanon
P.O. Box: 11-5020
Department of Matehmatics
Faculty of Science
Beirut Arab University
Beirut, Lebanon
P.O. Box: 11-5020
Department of Matehmatics
Faculty of Science
Beirut Arab University
Beirut, Lebanon
P.O. Box: 11-5020
AUTHOR
M
Abdulrahim
mna@bau.edu.lb
true
2
Professor
Department of Mathematics
Faculty of Science
Beirut Arab University
P.O. Box: 11-5020
Beirut, Lebanon
Professor
Department of Mathematics
Faculty of Science
Beirut Arab University
P.O. Box: 11-5020
Beirut, Lebanon
Professor
Department of Mathematics
Faculty of Science
Beirut Arab University
P.O. Box: 11-5020
Beirut, Lebanon
LEAD_AUTHOR
[1] D. Bessis, J. Michel, Explicit presentations for exceptional braid groups. Experiment. Math. 13 (3) (2004),
1
[2] J. Birman, Braids, Links and Mapping Class Groups. Annals of Mathematical Studies, Princeton University
2
Press, 82 (1975).
3
[3] M. Broue, G. Malle, R. Rouquier, Complex re ection groups, braid groups, Hecke algebras. J. reine angew.
4
Math. 500 (1998), 127-190.
5
[4] M. Chlouveraki, Degree and Valuation of the Schur elements of cyclotomic Hecke algebras J. Algebra, 320
6
(11) (2008), 3935-3949.
7
[5] A. Cohen, Finite complex re ection groups. Ann. Sci. Ecole Norm. Sup. (4), 9 (3) (1976), 379-436.
8
[6] I. Gordon, S. Grieth, Catalan numbers for complex re ection groups. Amer. J. Math., 134 (6) (2012),
9
1491-1502.
10
[7] G. Malle, J. Michel, Constructing representations of Hecke algebras for complex re ection groups. LMS J.
11
Comput. Math., 13 (2010), 426-450.
12
[8] G. Shephard, J. Todd, Finite unitary re ection groups. Canadian J. Math. 6 (1954), 274-304.
13
ORIGINAL_ARTICLE
Preorder Relators and Generalized Topologies
In this paper we investigate generalized topologies generated by a subbase ofpreorder relators and consider its application in the concept of the complement. We introducethe notion of principal generalized topologies obtained from the new type of open sets andstudy some of their important properties.
http://jlta.iauctb.ac.ir/article_528321_0f5b031391c1cfa5fc77f964b620a44b.pdf
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271
277
Generalized topology
preoerder relator
principal generalized topology
H
Arianpoor
arianpoor@tafreshu.ac.ir
true
1
Tafresh University. Iran.
Tafresh University. Iran.
Tafresh University. Iran.
LEAD_AUTHOR
[1] R. Baskaran, M. Murugalingam and D. Sivaraj, Lattice of generalized topology, Acta Math. Hungar., 133 (4)
1
(2011), 365-371.
2
[2] A. Csaszar, Foundations of General Topology, Pergamon Press, London, 1963.
3
[3] A. Csaszar, Generalized open sets, Acta Math. Hungar., 75 (1997), 65-87.
4
[4] A. Csaszar, Generalized topology, generalized continuity, Acta Math. Hungar., 96 (2002), 351-357.
5
[5] A. Csaszar, Ultratopologies generated by generalized topologies, Acta Math. Hungar., 110 (1-2) (2006), 153-
6
[6] E. Ekici and B. Roy, New generalized topologies on generalized topological spaces due to Csaszar, Acta Math.
7
Hungar., 132 (1-2) (2011), 117-124.
8
[7] R. E. Larson and S. J. Andima, The lattice of topologies: a survey, Rockey Mountain J. Math., 5 (2) (1975),177-198.[8] F. Lorrian, Notes on topological spaces with minimal neighborhoods, Amer. Math. Monthly, 76 (1969), 616-627.
9
[9] A. Szaz, Minimal structures, generalized topologies, and ascending systems should not be studied without
10
generalized uniformities, Filomat, 21 (2007), 87-97.
11
[10] A. K. Steiner, The lattice of topologies: structure and complementation, Trans. Amer. Math. Soc., 122 (1966),379-397.
12
ORIGINAL_ARTICLE
Dynamical distance as a semi-metric on nuclear conguration space
In this paper, we introduce the concept of dynamical distance on a nuclear con-guration space. We partition the nuclear conguration space into disjoint classes. This clas-sication coincides with the classical partitioning of molecular systems via the concept ofconjugacy of dynamical systems. It gives a quantitative criterion to distinguish dierentmolecular structures.
http://jlta.iauctb.ac.ir/article_528322_fdfa87a4e2657d31817ebb067fc65873.pdf
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279
287
Dynamical distance
molecular structure
nuclear conguration
QTAIM
M
Rahimi
m10.rahimi@gmail.com
true
1
Faculty of Science, Department of Mathematics, Qom University,
Qom, Iran.
Faculty of Science, Department of Mathematics, Qom University,
Qom, Iran.
Faculty of Science, Department of Mathematics, Qom University,
Qom, Iran.
LEAD_AUTHOR
[1] V. I. Arnold, Ordinary Dierential Equations, MIT Press 1973.
1
[2] R. F. W. Bader, Y. Tal, S. G. Anderson, T. T. Nguyen-Dang, Theory of Molecular Structure and its Change,
2
Isr. J. Chem. 19 (1980), 8-29.
3
[3] R. F. W. Bader, T. T. Nguyen-Dang, Y. Tal, S. G. Anderson, A topological theory of molecular structure,
4
Rep. Prog. Phys. 44 (1981), 893.
5
[4] R. F. W. Bader, S. G. Anderson, A. J. Duke, Quantum topology of molecular charge distributions. I, J. Am.
6
Chem. Soc. 101 (1979), 1389.
7
[5] R. F. W. Bader, T. T. Nguyen-Dang, Y. Tal, Quantum topology of molecular charge distributions. II. Molec-
8
ular structure and its change, J. Chem. Phys. 70 (1979), 4316.
9
[6] R. F. W. Bader, P. J. MacDougall, C. D. H. Lau, Bonded and nonbonded charge concentrations and their
10
relation to molecular geometry and reactivity, J. Am. Chem. Soc. 106 (1984), 1594-1605.
11
[7] R. F. W. Bader, R. J. Gillespie, P. J. MacDougall, A physical basis for the VSEPR model of molecular
12
geometry, J. Am. Chem. Soc. 110 (1988), 7329-7336.
13
[8] R. F. W. Bader, Atoms in Molecules: A Quantum Theory, Oxford University Press, Oxford, UK 1990.
14
[9] H.W. Broer, F. Dumortier, S .J. van Strien, F. Takens, Structures in Dynamics Studies in Mathematical
15
Physics, vol. 2, Elsevier Science Publishing Company, North-Holland 1991.
16
[10] K. Collard, G. G. Hall, Orthogonal trajectories of the electron density, Int. J. Quantum Chem. 12 (1977),
17
[11] S. H. Friedberg, A. J. Insel, L. E. Spence, Linear Algebra, 3th Edition, Prentice Hall 2003.
18
[12] M. W. Hirsch, S. Smale, R. L. Devaney, Dierential Equations, Dynamical Systems, and An Introduction to
19
Chaos, Elsevier Academic Press 2004.
20
[13] T. A. Keith, R. F. W. Bader, Y. Aray, Structural homeomorphism between the electron density and the virial
21
eld, Int. J. Quantum chem. 57 (1996), 183-198.
22
[14] H. J. Korsch, H. J. Jodi, Chaos; a program collection for the PC, Springer-Verlag 1998.
23
[15] P. G. Mezey, Catchment region partitioning of energy hypersurfaces, I, Theor. Chim. Acta. 58 (1981), 309-330.
24
[16] P. G. Mezey, Potential Energy Hyper-surfaces, Elsevier, Amsterdom 1987.
25
[17] P. Nasertayoob, Sh. Shahbazian, The topological analysis of electronic charge densities: A reassessment of
26
foundations, Journal of Molecular Structure (THEOCHEM) 896 (2008), 53-58.
27
[18] T. T. Nguyen-Dang, R. F. W. Bader, A theory of molecular structure, Physica A. 114 (1982), 68.
28
[19] J. Palis, S. Smale, Proc. Symp. Pure Math. Am. Math. Soc. 14 (1970), 223.
29
[20] P. L. A Popelier, On the full topology of the Laplacian of the electron density, Coord. Chem. Rev. 197 (2000),
30
[21] T. Poston, I. Stewart, Catastrophe Theory and its Applications, Pitman, London 1978.
31
[22] M. Rahimi, P. Nasertayoob, Dynamical information content of the molecular structures: A quantum theory
32
of atoms in molecules (QTAIM) approach, MATCH Commun. Math. Comput. Chem. 67 (2012), 109-126.
33
[23] C. Robinson, Dynamical Systems, Stability, Symbolic Dynamics and Chaos, CRC press 1994.
34
[24] Y. Tal, R. F. W. Bader, T. T. Nguyen-Dang, S. G. Anderson, Quantum topology. IV. Relation between the
35
topological and energetic stabilities of molecular structures, J. Chem. Phys. 74 (1981), 51-62.
36
[25] Y. Tal, R. F. Bader, J. Erkku, Structural homeomorphism between the electronic charge density and the
37
nuclear potential of a molecular system, Phys. Rev. A. 21 (1980), 1-11.
38
[26] R. Thom, Structural stability and Morphogenesis, W. A. Benjamin, Reading, Massachusett 1975.
39
ORIGINAL_ARTICLE
On the commuting graph of some non-commutative rings with unity
Let R be a non-commutative ring with unity. The commuting graph of $R$ denoted by $\Gamma(R)$, is a graph with a vertex set $R\setminus Z(R)$ and two vertices $a$ and $b$ are adjacent if and only if $ab=ba$. In this paper, we investigate non-commutative rings with unity of order $p^n$ where $p$ is prime and $n \in \lbrace 4,5 \rbrace$. It is shown that, $\Gamma(R)$ is the disjoint union of complete graphs. Finally, we prove that there are exactly five commuting graphs of non-commutative rings with unity up to twenty vertices and they are $3K_2,3K_4,7K_2, K_2 \cup 2K_6$ and $4K_2 \cup K_6$.
http://jlta.iauctb.ac.ir/article_528323_4e4b648974af985b7d19b5295b6aec8a.pdf
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289
294
Commuting graphs
non-commutative rings
non-connected graphs
F
Ramezani
f.ramezani988@gmail.com
true
1
Department of Basic science , Imam Khomeini International University, Qazvin, Iran.
Department of Basic science , Imam Khomeini International University, Qazvin, Iran.
Department of Basic science , Imam Khomeini International University, Qazvin, Iran.
LEAD_AUTHOR
E
Vatandoost
e_vatandoost@sci.ikiu.ac.ir
true
2
Department of Basic science , Imam Khomeini International University, Qazvin, Iran.
Department of Basic science , Imam Khomeini International University, Qazvin, Iran.
Department of Basic science , Imam Khomeini International University, Qazvin, Iran.
AUTHOR
[1] A. Abdollahi, Commuting graphs of full matrix rings over nite elds. Linear Algebra and its Applications.
1
428 (11) (2008), 2947-2954.
2
[2] S. Akbari, M. Ghandehari, M. Hadian, A. Mohammadian, On commuting graphs of semisimple rings. Linear
3
algebra and its applications. 390 (2004), 345-355.
4
[3] S. Akbari, A. Mohammadian, H. Radjavi, P. Raja, On the diameters of commuting graphs. Linear algebra
5
and its applications. 418(1) (2006), 161{176
6
[4] S. Akbari, P. Raja, Commuting graphs of some subsets in simple rings. Linear algebra and its applications.
7
416 (2) (2006), 1038-1047.
8
[5] N. Biggs, Algebraic Graph Theory. Cambridge University Press, Cambridge, 1993.
9
[6] K. E. Eldridge, Orders for nite noncommutative rings with unity. American Mathematical Monthly. (1968),
10
[7] G. R. Omidi, E. Vatandoost, On the commuting graph of rings. Journal of Algebra and Its Applications. 10
11
(03) (2011), 521-527.
12
[8] E. Vatandoost, F. Ramezani , A. Bahraini, On the commuting graph of non-commutative rings of order pnq.
13
J. Linear. Topol. Algebra, 03 (01) (2014), 1-6.
14