ORIGINAL_ARTICLE
DOMINATION NUMBER OF TOTAL GRAPH OF MODULE
Let $R$ be a commutative ring and $M$ be an $R$-module with $T(M)$ as subset, the set of torsion elements. The total graph of the module denoted by $T(\Gamma(M))$, is the (undirected) graph with all elements of $M$ as vertices, and for distinct elements $n,m \in M$, the vertices $n$ and $m$ are adjacent if and only if $n+m \in T(M)$. In this paper we study the domination number of $T(\Gamma(M))$ and investigate the necessary conditions for being $\mathbb{Z}_{n}$ as module over $\mathbb{Z}_{m}$ and we find the domination number of $T(\Gamma(\mathbb{Z}_{n}))$.
http://as.yazd.ac.ir/article_665_fa2f8c151be2c96db3d6e8ef1e2c192f.pdf
2015-02-01T11:23:20
2018-12-19T11:23:20
1
9
total graph
domination number
module
Abbas
Shariatnia
true
1
Islamic Azad University, Tehran, Iran
Islamic Azad University, Tehran, Iran
Islamic Azad University, Tehran, Iran
LEAD_AUTHOR
Abolfazl
Tehranian
tehranian1340@yahoo.com
true
2
Islamic Azad University
Islamic Azad University
Islamic Azad University
AUTHOR
[1] D. F. Anderson and A. Badawi, The total graph of a commutative ring, J. Algebra 320 (2008), 2706{2719.
1
[2] D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217 (1999), 434{447.
2
[3] D. D. Anderson and M. Naseer, Beck's coloring of a commutative ring, J. Algebra 159 (1993), 500{514.
3
[4] I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), 208{226.
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[5] M. Axtell and J. Stickles, Zero-divisor graphs of idealizations, J. Pure Appl. Algebra, 204 (2006), 235{243.
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[6] S. Ebrahimi Atani and S. Habibi The total torsion element graph of a module over a commutative ring, Analele Stiintice ale Universitatii Ovidius Constanta, 19( 1)(2011), 2334.
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[7] M. R. Garey, D. S. Johnson, Computers and Intractability. A Guide to the Theory of NPCompleteness, A Series of Books in the Mathematical Sciences, W. H. Freeman and Co., San Francisco, Calif., 1979.
7
[8] T. W. Haynes, S. T. Hedetniemi, P. J. Slater, Fundamentals of Domination in Graphs, Monographs and Textbooks in Pure and Applied Mathematics, 208, Marcel Dekker, Inc., New York, 1998.
8
[9] T. W. Haynes, S. T. Hedetniemi, P. J. Slater (Editors), Domination in Graphs. Advanced Topics, Monographs and Textbooks in Pure and Applied Mathematics, 209, Marcel Dekker, Inc., New York, 1998.
9
[10] H. R. Maimani, C. Wickham, S. Yassemi, Rings whose total graphs have genus at most one, Rocky Mountain J. Math. 42 (2012), 1551{1560.
10
[11] M. H. Shekarriza, M. H. Shirdareh Haghighi and H. Sharif, On the Total Graph of a Finite Commutative Ring , Comm. Algebra 40(8) (2012), 2798{2807.
11
ORIGINAL_ARTICLE
A note on vague graphs
In this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. Also, density and balanced irregular vague graphs are discussed and some of their properties are established. Finally we give an application of vague digraphs.
http://as.yazd.ac.ir/article_666_3ce42facef7525e9f7e690c4d5a47d4e.pdf
2015-02-01T11:23:20
2018-12-19T11:23:20
11
22
Vague graph
density
balanced irregular vague graph
product vague graph
H.
Rashmanlou
true
1
Islamic Azad University, Central Tehran Branch
Islamic Azad University, Central Tehran Branch
Islamic Azad University, Central Tehran Branch
AUTHOR
R.A.
Borzooei
true
2
Shahid Beheshti University
Shahid Beheshti University
Shahid Beheshti University
AUTHOR
[1]M. Akram, N. Gani and A. Borumand Saeid, Vague hypergraphs, Journal of Intelligent and Fuzzy Systems, 26, 647–653 (2014).
1
[2] M. Akram, F. Feng, S. Sarwar and Y.B. Jun, Certain types of vague graphs, University Politehnica of Bucharest Scientific Bulletin Series A, 76 (1), 141–154 (2014).
2
[3] R. A. Borzooei and H. Rashmanlou, Ring sum in product intuitionistic fuzzy graphs, Journal of advanced research in pure mathematics, 7 (1), 16–31 (2015).
3
[4] R. A. Borzooei and H. Rashmanlou, Domination in vague graphs and its applications, Journal of Intelligent and Fuzzy Systems, to appear.
4
[5] R. A. Borzooei and H. Rashmanlou, Degree of vertices in vague graphs, Journal of applied mathematics and informatics, to appear.
5
[6] W.-L. Gau and D. J. Buehrer, Vague sets, IEEE Transactions on Systems, Man and Cybernetics, 23 (2), 610–614 (1993).
6
[7] A. Kaufman, Introduction a la Theorie des Sous-Emsembles Flous, Vol. 1, Masson et Cie, 1973.
7
[8] J. N. Mordeson and P. S. Nair, Fuzzy Graphs and Fuzzy Hypergraphs, Physica, Heidelberg, Germany, 2nd edition, 2001.
8
[9] M. Pal and H. Rashmanlou, Irregular interval- valued fuzzy graphs, Annals of Pure and Applied Mathematics, 3 (1),
9
56–66 (2013).
10
[10] N. Ramakrishna,Vague graphs, International Journal of Computational Cognition, 7, 51–58 (2009).
11
[11] H. Rashmanlou and M. Pal, Antipodal interval-valued fuzzy graphs, International Journal of Applications of Fuzzy Sets and Artificial Intelligence, 3, 107–130 (2013).
12
[12] H. Rashmanlou and M. Pal, Balanced interval-valued fuzzy graph, Journal of Physical Sciences, 17, 43–57 (2013).
13
[13] H. Rashmanlou and M. Pal, Some properties of highly irregular interval-valued fuzzy graphs, World Applied Sciences Journal, 27 (12), 1756–1773 (2013).
14
[14] H. Rashmanlou, S. Samanta, M. Pal and R. A. Borzooei, A study on bipolar fuzzy graphs, Journal of Intelligent and Fuzzy Systems, 28, 571–580 (2015).
15
[15] H. Rashmanlou and Y. B. Jun, Complete interval-valued fuzzy graphs, Annals of Fuzzy Mathematics and Informatics, 6 (3), 677–687 (2013).
16
[16] A. Rosenfeld, Fuzzy graphs, Fuzzy Sets and their Applications (L. A. Zadeh, K. S. Fu, and M. Shimura, Eds.), Academic Press, New York, 77–95, 1975.
17
[17] S. Samanta and M. Pal, Fuzzy tolerance graphs, International Journal Latest Trend Math, 1 (2), 57–67 (2011).
18
[18] S. Samanta and M. Pal, Fuzzy threshold graphs, CiiT International Journal of Fuzzy Systems, 3 (12), 360–364 (2011).
19
[19] A. A. Talebi, H. Rashmanlou, N. Mehdipoor, Isomorphism on vague graphs, Annals of Fuzzy Mathematics and Informatics, 6 (3), 575–588 (2013).
20
[20] A. A. Talebi, N. Mehdipoor, H. Rashmanlou, Some operations on vague graphs, Journal of Advanced Research in Pure Mathematics, 6 (1), 61–77 (2014).
21
[21] L. A. Zadeh, Fuzzy sets, Information and Control 8, 338–353 (1965).
22
[22] L. A. Zadeh, Similarity relations and fuzzy ordering, Information Sciences, 3, 177–200 (1971).
23
[23] L. A. Zadeh, Is there a need for fuzzy logical, Information Sciences, 178 , 2751–2779 (2008).
24
ORIGINAL_ARTICLE
ON NEW CLASSES OF MULTICONE GRAPHS DETERMINED BY THEIR SPECTRUMS
A multicone graph is defined to be join of a clique and a regular graph. A graph $ G $ is cospectral with graph $ H $ if their adjacency matrices have the same eigenvalues. A graph $ G $ is said to be determined by its spectrum or DS for short, if for any graph $ H $ with $ Spec(G)=Spec(H)$, we conclude that $ G $ is isomorphic to $ H $. In this paper, we present new classes of multicone graphs that are DS with respect to their spectrums. Also, we show that complement of these graphs are DS with respect to their adjacency spectrums. In addition, we show that graphs cospectral with these graphs are perfect. Finally, we find automorphism group of these graphs and one conjecture for further researches is proposed.
http://as.yazd.ac.ir/article_667_092a146cd741a0833839870c5e8d913f.pdf
2015-02-01T11:23:20
2018-12-19T11:23:20
23
34
Adjacency spectrum
Laplacian spectrum
Multicone graph
DS graph
Automorphism group
Ali
Zeydi Abdian
azeydiabdi@gmail.com
true
1
Lorestan University
Lorestan University
Lorestan University
LEAD_AUTHOR
S. Morteza
Mirafzal
true
2
Lorestan University
Lorestan University
Lorestan University
AUTHOR
[1] A. Abdollahi, S. Janbaz and M. Oubodi, Graphs Cospectral with A Friendship Graph Or its Complement, Trans. Combin. Vol. 2 No. 4 (2013), pp. 37–52.
1
[2] N. L. Biggs, Algebraic Graph Theory, (second edition), Cambridge University press, cambridge, (1933). [3] X. M. Cheng, G. R. W. Greaves, J. H. Koolen, Graphs with three eigenvalues and second largest eigenvalue at most 1, http://de.arxiv.org/abs/1506.02435v1.
2
[4] D. Cvetkovi´c, P. Rowlinson and S. Simi´c, An Introduction to the theory of graph spectra, London Mathematical Society Student Texts, 75, Cambridge University Press, Cambridge, 2010.
3
[5] J. D. Dixon and B. Mortimer, Permutation Groups, Math. Proc. Cambridge Phil. Soc. (1998).
4
[6] G. H. Fath-Tabar, The Automorphism Group Of Finite Graphs, Iran. J. Math. Sci. Inf., (2007), 29–33.
5
[7] A. Ganasem, Automorphism groups of graphs, ArXiv: 1206. 6279v1 (2012).
6
[8] A. Ganasem, Automorphism of Cayley graph generated by transposition sets, arXiv 1303.5974v2.
7
[9] C. D. Godsil, On the full automorphism group of a graph, Combinatorica, 1 (1981) 243–256.
8
[10] C. Godsil and G. Royle, Algebraic Graph Theory, Springer-Verlag, New York, 2001
9
[11] U. Kanauer, Algebraic Graph Theory, Morphism, Monoids and Matrices, (2011).
10
[12] B. Liu, On an upper bound of the spectral radius of graphs, Discrete Mathematics 308 (2008) 5317–5324.
11
[13] R. Merris, Laplacian graph eigenvectors, Linear Algebra Appl. 278 (1998), 221–236.
12
[14] A. Mohammadian, B. Tayfeh Rezaie, Graphs with four distinct Laplacian eigenvalues, J. Algebraic Combin. 34 (2011), 671–682.
13
[15] G. R. Omidi, On graphs with largest Laplacian eignnvalues at most 4, Australas. J. Combin., 44 (2009) 163–170.
14
[16] E. R. van Dam and W. H. Haemers, Which Graphs are determined by their spectrum?, Linear Alg. Appl. 373 (2003) 241–272.
15
[17] E. R. van Dam, Willem H. Haemers, Developments on spectral characterizations of graphs, Discrete Math., 309 (2009) 576–586.
16
[18] J. F. Wang, H. Zhao ,Q. Haung , Spectral Charactrization of Multicone Graphs. Czec. Math. J., 62 137 (2012), 117–126. 32
17
[19] J. Wang, Q. Huang, Spectral Characterization of Generalized Cocktail-Party Graphs. J. Math. Research Appl., (2012), Vol. 32, No. 6, pp. 666–672.
18
[20] D.B. West, Introduction to Graph Theory (Second Edition), University of Illinios—Urbana (2001)
19
ORIGINAL_ARTICLE
Uniformly classical quasi-primary submodules
In this paper we introduce the notions of uniformly quasi-primary ideals and uniformly classical quasi-primary submodules that generalize the concepts of uniformly primary ideals and uniformly classical primary submodules; respectively. Several characterizations of classical quasi-primary and uniformly classical quasi-primary submodules are given. Then we investigate for a ring $R$, when any finite intersection of (uniformly) primary submodules of any $R$-module is a (uniformly) classical quasi-primary submodule. Furthermore, the behavior of classical quasi-primary and uniformly classical quasi-primary submodules under localizations are studied. Also, we investigate the existence of (minimal) primary submodules containing classical quasi-primary submodules.
http://as.yazd.ac.ir/article_668_3985baca23a24ea768e39fc781fa4b2c.pdf
2015-02-01T11:23:20
2018-12-19T11:23:20
35
47
Classical quasi-primary
Uniformly classical quasi-primary
M.H.
Naderi
true
1
University of Qom
University of Qom
University of Qom
LEAD_AUTHOR
[1] R. E. Atani and S. E. Atani, A note on uniformly primary submodules, Novi SAD J. Math. 38 (2) (2008) 83-89.
1
[2] S. E. Atani and A. Y. Darani, On quasi-primary submodules, Chiang Mai J. Science 33 (3) (2006) 249-254.
2
[3] M. F. Atiyah and I. G. MacDonald, Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, 1969.
3
[4] A. Azizi, On prime and weakly prime submodules, Vietnam J. Math. 36 (3) (2008) 315-325.
4
[5] M. Baziar and M. Behboodi, Classical primary submodules and decomposition theory of modules, J. Algebra Appl. 8 (3) (2009) 351-362.
5
[6] M. Baziar, M. Behboodi and H. Sharif, Uniformly classical primary submodules, Comm. Algebra 40 (2012) 3192-3201.
6
[7] M. Behboodi, R. Jahani-Nezhad, and M. H. Naderi, Classical quasi-primary submodules, Bull. Iranian Math. Soc.37 (4) (2011) 51-71.
7
[8] M. Behboodi, R. Jahani-Nezhad, and M. H. Naderi, Quasi-primary decomposition in modules over Prufer domains, Journal of Algebraic Systems 1 (2) (2013) 149-160.
8
[9] J. A. Cox and A. J. Hetzel, Uniformly primary ideals, J. Pure Appl. Algebra 212 (1) (2008) 1-8.
9
[10] L. Fuchs, On quasi-primary ideals, Acta Sci. Math. (Szeged) 11 (1947) 174-183.
10
[11] L. Fuchs and E. Mosteig, Ideal theory in Prufer domains, J. Algebra 252 (2002) 411-430.
11
[12] R. Y. Sharp, Steps in commutative algebra, London Math. Soc. Cambridge University Press, Cambridge, 1990.
12
ORIGINAL_ARTICLE
On transitive soft sets over semihypergroups
The aim of this paper is to initiate and investigate new soft sets over semihypergroups, named special soft sets and transitive soft sets and denoted by $S_{H}$ and $T_{H},$ respectively. It is shown that $T_{H}=S_{H}$ if and only if $\beta=\beta^{*}.$ We also introduce the derived semihypergroup from a special soft set and study some properties of this class of semihypergroups.
http://as.yazd.ac.ir/article_678_9dbafd641c22d9dc4190caffde36426d.pdf
2015-02-01T11:23:20
2018-12-19T11:23:20
49
58
soft sets
transitive soft sets
(semi)hypergroup
strongly regular relation
M.
Jafarpour
true
1
Vali-e-Asr University
Vali-e-Asr University
Vali-e-Asr University
LEAD_AUTHOR
V.
Vahedi
true
2
Vali-e-Asr University
Vali-e-Asr University
Vali-e-Asr University
AUTHOR
[1] P. Corsini, {it Prolegomena of Hypergroup Theory}, Aviani Editore, Tricesimo, 1993.
1
[2] P. Corsini, and V. Leoreanu, {it Applications of Hyperstructure Theory}, Kluwer Academical Publications, Dordrecht, 2003.
2
[3] B. Davvaz, V. Leoreanu-Fotea, {it Hyperring Theory and Applications}, International Academic Press, USA, 2007.
3
[4] F. Feng, Y.M. Li, V. Leoreanu-Fotea, Application of level soft sets in
4
decision making based on interval-valued fuzzy soft sets, Computers and
5
Mathematics with Applications 60 (2010) 1756-1767.
6
[5] F. Feng, Y.B. Jun, X.Y. Liu, L.F. Li, An adjustable approach to fuzzy
7
soft set based decision making, Journal of Computational and Applied
8
Mathematics 234 (2010) 10-20.
9
[6] F. Feng, X.Y. Liu, V. Leoreanu-Fotea, Y.B. Jun, Soft sets and soft rough
10
sets, Information Sciences 181 (2011) 1125-1137.
11
[7] F. Feng, Y.M. Li, N. Cagman, Generalized uni-int decision making
12
schemes based on choice value soft sets, European Journal of Operational
13
Research 220 (2012) 162-170.
14
[8] D. Freni, {it Une note sur le cÂœur d'un hypergroupe et sur la cl^{o}ture transitive
15
$betasp ast$ de $beta$. (French) [A note on the core of a
16
hypergroup and the transitive closure $betasp ast$ of
17
$beta$]}, Riv. Mat. Pura Appl., 8 (1991) 153-156.
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[9] M. Koskas, Groupes et hypergroupes homomorphes a un
19
demi-hypergroupe, C. R. Acad Sc., Paris, 257 (1963), 334-337.
20
bibitem{4}
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[10] P.K. Maji, A.R. Roy, R. Biswas, An application of soft sets in a decision
22
making problem, Computers and Mathematics with Applications 44 (2002) 1077-
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[11] F. Marty, {it Sur une Generalization de la Notion de Groupe}, 8th Congress
24
Math. Scandenaves, Stockholm, Sweden, (1934) 45-49.
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[12] D. Molodtsov, Soft set theory first results, Comput. Math. Appl. 37 (1999) 19Â–31.
26
[13]T. Vougiouklis, {it Hyperstructures and Their Representations}, Hadronic
27
Press, Palm Harbor, FL, 1994.
28
ORIGINAL_ARTICLE
Similarity DH-Algebras
In \cite{GL}, B. Gerla and I. Leu\c{s}tean introduced the notion of similarity on MV-algebra. A similarity MV-algebra is an MV-algebra endowed with a binary operation $S$ that verifies certain additional properties. Also, Chirte\c{s} in \cite{C}, study the notion of similarity on \L ukasiewicz-Moisil algebras. In particular, strong similarity \L ukasiewicz-Moisil algebras were defined. In this paper we define and study the variety of similarity symmetric Heyting algebras (or similarity DH-algebras), i.e. symmetric Heyting algebras endowed with an operation of similarity $S$. These algebras are a generalization of strong similarity \L ukasiewicz-Moisil algebras. In addition, we introduce a propositional calculus and prove this calculus has similarity DH-algebras as algebraic counterpart.
http://as.yazd.ac.ir/article_726_d6a28c0095f8cebd1b83c7fef91962da.pdf
2015-02-01T11:23:20
2018-12-19T11:23:20
59
71
symmetric Heyting algebras
Similarity
$S$--filter
Federico
Gabriel Alminana
true
1
Universidad Nacional de San Juan, Argentina.
Universidad Nacional de San Juan, Argentina.
Universidad Nacional de San Juan, Argentina.
LEAD_AUTHOR
Mathias
Exequiel Pelayes
true
2
Universidad Nacional de San Juan, Argentina.
Universidad Nacional de San Juan, Argentina.
Universidad Nacional de San Juan, Argentina.
AUTHOR
[1] V. Boicescu, A. Filipoiu, G. Georgescu and S. Rudeanu, Lukasiewicz-Moisil Algebras, Anals of Discrete Mathematics, 49, North-Holland, The Netherlands, 1991.
1
[2] J.L. Castro, F. Klawonn, Similarity in Fuzzy Reasoning, using Fuzzy Logic. Mathware and Soft Computing, 2:
2
197-228, 1995.
3
[3] G. Cattaneo, D. Ciucci, R. Giuntini, M. Konig. Algebraic structures related to many valued logical systems. I. Heyting Wajsberg algebras. Fund. Inform. 63 (2004), no. 4, 331-355.
4
[4] F. Chirtes, Similarity Lukasiewicz{Moisil algebras, An. Univ. Craiova Ser. Mat. Inform. 35 (2008), 54-75.
5
[5] F. Formato, G. Gerla, M. Sessa, Similarity-based unication, Fundamenta Informaticae, 41: 393-414, 2000.
6
[6] G. Georgescu, A. Popescu, Concept lattices and similarity in non-commutative fuzzy logic, Fundamenta Informaticae, 53: 23-54, 2002.
7
[7] B. Gerla and I. Leustean, Similarity MV{algebras, Fund. Inform. 69 (2006), no. 3, 287-300.
8
[8] A. Monteiro, Sur les algebres de Heyting Simetriques, Special issue in honor of Antonio Monteiro. Portugal. Math. 39(1{4), 1980.
9
[9] L. Pasi, S. Kalle, Fuzzy similarity based classication in normal Lukasiewicz algebra with geometric and harmonicmean, Third eusat, an international conference in fuzzy logic and technology, Zittau, Saks. (2003) 242-245.
10
[10] A. Rodrguez, A. Torrens, V. Verdu. Lukasiewicz logic and Wajsberg algebras. Polish Acad. Sci. Inst. Philos. Sociol. Bull. Sect. Logic 19 (1990), no. 2, 51-55.
11
[11] H.P. Sankappanavar, Heyting algebras with a dual lattice endomorphism, Z. Math. Logik Grundlag. Math. 33 (1987), no. 6, 565-573.
12
[12] E. Turunen, A Lukasiewicz-style many-valued similarity reasoning. Review. in Beyond Two: Theory and Applications of Multiple Valued Logic, Melvin Fitting and Ewa Orlowska editors, 311-321, 2003.
13
[13] L. Zadeh, Similarity relations and fuzzy orderings, Information Sciences, 3: 177-200, 1971.
14