2015
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1
1
0
DOMINATION NUMBER OF TOTAL GRAPH OF MODULE
2
2
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 $T(Gamma(mathbb{Z}_{n}))$.
1

1
9


Abbas
Shariatnia
Islamic Azad University, Tehran, Iran
Islamic Azad University, Tehran, Iran
Iran


Abolfazl
Tehranian
Islamic Azad University
Islamic Azad University
Iran
tehranian1340@yahoo.com
total graph
domination number
module
[[1] D. F. Anderson and A. Badawi, The total graph of a commutative ring, J. Algebra 320 (2008), 2706{2719.##[2] D. F. Anderson and P. S. Livingston, The zerodivisor graph of a commutative ring, J. Algebra 217 (1999), 434{447.##[3] D. D. Anderson and M. Naseer, Beck's coloring of a commutative ring, J. Algebra 159 (1993), 500{514.##[4] I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), 208{226.##[5] M. Axtell and J. Stickles, Zerodivisor graphs of idealizations, J. Pure Appl. Algebra, 204 (2006), 235{243.##[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.##[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.##[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.##[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.##[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.##[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. ##]
A note on vague graphs
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2
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.
1

11
22


H.
Rashmanlou
Islamic Azad University, Central Tehran Branch
Islamic Azad University, Central Tehran Branch
Iran


R.A.
Borzooei
Shahid Beheshti University
Shahid Beheshti University
Iran
Vague graph
density
balanced irregular vague graph
product vague graph
[[1]M. Akram, N. Gani and A. Borumand Saeid, Vague hypergraphs, Journal of Intelligent and Fuzzy Systems, 26, 647–653 (2014).##[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).##[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).##[4] R. A. Borzooei and H. Rashmanlou, Domination in vague graphs and its applications, Journal of Intelligent and Fuzzy Systems, to appear.##[5] R. A. Borzooei and H. Rashmanlou, Degree of vertices in vague graphs, Journal of applied mathematics and informatics, to appear.##[6] W.L. Gau and D. J. Buehrer, Vague sets, IEEE Transactions on Systems, Man and Cybernetics, 23 (2), 610–614 (1993).##[7] A. Kaufman, Introduction a la Theorie des SousEmsembles Flous, Vol. 1, Masson et Cie, 1973.##[8] J. N. Mordeson and P. S. Nair, Fuzzy Graphs and Fuzzy Hypergraphs, Physica, Heidelberg, Germany, 2nd edition, 2001.##[9] M. Pal and H. Rashmanlou, Irregular interval valued fuzzy graphs, Annals of Pure and Applied Mathematics, 3 (1),##56–66 (2013).##[10] N. Ramakrishna,Vague graphs, International Journal of Computational Cognition, 7, 51–58 (2009).##[11] H. Rashmanlou and M. Pal, Antipodal intervalvalued fuzzy graphs, International Journal of Applications of Fuzzy Sets and Artificial Intelligence, 3, 107–130 (2013).##[12] H. Rashmanlou and M. Pal, Balanced intervalvalued fuzzy graph, Journal of Physical Sciences, 17, 43–57 (2013).##[13] H. Rashmanlou and M. Pal, Some properties of highly irregular intervalvalued fuzzy graphs, World Applied Sciences Journal, 27 (12), 1756–1773 (2013).##[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] H. Rashmanlou and Y. B. Jun, Complete intervalvalued fuzzy graphs, Annals of Fuzzy Mathematics and Informatics, 6 (3), 677–687 (2013).##[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] S. Samanta and M. Pal, Fuzzy tolerance graphs, International Journal Latest Trend Math, 1 (2), 57–67 (2011).##[18] S. Samanta and M. Pal, Fuzzy threshold graphs, CiiT International Journal of Fuzzy Systems, 3 (12), 360–364 (2011).##[19] A. A. Talebi, H. Rashmanlou, N. Mehdipoor, Isomorphism on vague graphs, Annals of Fuzzy Mathematics and Informatics, 6 (3), 575–588 (2013).##[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] L. A. Zadeh, Fuzzy sets, Information and Control 8, 338–353 (1965).##[22] L. A. Zadeh, Similarity relations and fuzzy ordering, Information Sciences, 3, 177–200 (1971).##[23] L. A. Zadeh, Is there a need for fuzzy logical, Information Sciences, 178 , 2751–2779 (2008). ##]
ON NEW CLASSES OF MULTICONE GRAPHS DETERMINED BY THEIR SPECTRUMS
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2
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.
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23
34


Ali
Zeydi Abdian
Lorestan University
Lorestan University
Iran
azeydiabdi@gmail.com


S. Morteza
Mirafzal
Lorestan University
Lorestan University
Iran
Adjacency spectrum
Laplacian spectrum
Multicone graph
DS graph
Automorphism group
[[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. ##[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. ##[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. ##[5] J. D. Dixon and B. Mortimer, Permutation Groups, Math. Proc. Cambridge Phil. Soc. (1998). ##[6] G. H. FathTabar, The Automorphism Group Of Finite Graphs, Iran. J. Math. Sci. Inf., (2007), 29–33. ##[7] A. Ganasem, Automorphism groups of graphs, ArXiv: 1206. 6279v1 (2012). ##[8] A. Ganasem, Automorphism of Cayley graph generated by transposition sets, arXiv 1303.5974v2. ##[9] C. D. Godsil, On the full automorphism group of a graph, Combinatorica, 1 (1981) 243–256. ##[10] C. Godsil and G. Royle, Algebraic Graph Theory, SpringerVerlag, New York, 2001 ## [11] U. Kanauer, Algebraic Graph Theory, Morphism, Monoids and Matrices, (2011). ##[12] B. Liu, On an upper bound of the spectral radius of graphs, Discrete Mathematics 308 (2008) 5317–5324. ##[13] R. Merris, Laplacian graph eigenvectors, Linear Algebra Appl. 278 (1998), 221–236. ##[14] A. Mohammadian, B. Tayfeh Rezaie, Graphs with four distinct Laplacian eigenvalues, J. Algebraic Combin. 34 (2011), 671–682. ##[15] G. R. Omidi, On graphs with largest Laplacian eignnvalues at most 4, Australas. J. Combin., 44 (2009) 163–170. ##[16] E. R. van Dam and W. H. Haemers, Which Graphs are determined by their spectrum?, Linear Alg. Appl. 373 (2003) 241–272. ##[17] E. R. van Dam, Willem H. Haemers, Developments on spectral characterizations of graphs, Discrete Math., 309 (2009) 576–586. ##[18] J. F. Wang, H. Zhao ,Q. Haung , Spectral Charactrization of Multicone Graphs. Czec. Math. J., 62 137 (2012), 117–126. 32 ##[19] J. Wang, Q. Huang, Spectral Characterization of Generalized CocktailParty Graphs. J. Math. Research Appl., (2012), Vol. 32, No. 6, pp. 666–672. ##[20] D.B. West, Introduction to Graph Theory (Second Edition), University of Illinios—Urbana (2001) ##]
Uniformly classical quasiprimary submodules
2
2
In this paper we introduce the notions of uniformly quasiprimary ideals and uniformly classical quasiprimary submodules that generalize the concepts of uniformly primary ideals and uniformly classical primary submodules; respectively. Several characterizations of classical quasiprimary and uniformly classical quasiprimary 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 quasiprimary submodule. Furthermore, the behavior of classical quasiprimary and uniformly classical quasiprimary submodules under localizations are studied. Also, we investigate the existence of (minimal) primary submodules containing classical quasiprimary submodules.
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35
47


M.H.
Naderi
University of Qom
University of Qom
Iran
Classical quasiprimary
Uniformly classical quasiprimary
[[1] R. E. Atani and S. E. Atani, A note on uniformly primary submodules, Novi SAD J. Math. 38 (2) (2008) 8389.##[2] S. E. Atani and A. Y. Darani, On quasiprimary submodules, Chiang Mai J. Science 33 (3) (2006) 249254.##[3] M. F. Atiyah and I. G. MacDonald, Introduction to commutative algebra, AddisonWesley Publishing Co., Reading, Mass.LondonDon Mills, 1969.##[4] A. Azizi, On prime and weakly prime submodules, Vietnam J. Math. 36 (3) (2008) 315325.##[5] M. Baziar and M. Behboodi, Classical primary submodules and decomposition theory of modules, J. Algebra Appl. 8 (3) (2009) 351362.##[6] M. Baziar, M. Behboodi and H. Sharif, Uniformly classical primary submodules, Comm. Algebra 40 (2012) 31923201.##[7] M. Behboodi, R. JahaniNezhad, and M. H. Naderi, Classical quasiprimary submodules, Bull. Iranian Math. Soc.37 (4) (2011) 5171.##[8] M. Behboodi, R. JahaniNezhad, and M. H. Naderi, Quasiprimary decomposition in modules over Prufer domains, Journal of Algebraic Systems 1 (2) (2013) 149160.##[9] J. A. Cox and A. J. Hetzel, Uniformly primary ideals, J. Pure Appl. Algebra 212 (1) (2008) 18.##[10] L. Fuchs, On quasiprimary ideals, Acta Sci. Math. (Szeged) 11 (1947) 174183.##[11] L. Fuchs and E. Mosteig, Ideal theory in Prufer domains, J. Algebra 252 (2002) 411430.##[12] R. Y. Sharp, Steps in commutative algebra, London Math. Soc. Cambridge University Press, Cambridge, 1990. ##]
On transitive soft sets over semihypergroups
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2
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.
1

49
58


M.
Jafarpour
ValieAsr University
ValieAsr University
Iran


V.
Vahedi
ValieAsr University
ValieAsr University
Iran
soft sets
transitive soft sets
(semi)hypergroup
strongly regular relation
[[1] P. Corsini, {it Prolegomena of Hypergroup Theory}, Aviani Editore, Tricesimo, 1993.##[2] P. Corsini, and V. Leoreanu, {it Applications of Hyperstructure Theory}, Kluwer Academical Publications, Dordrecht, 2003.##[3] B. Davvaz, V. LeoreanuFotea, {it Hyperring Theory and Applications}, International Academic Press, USA, 2007.##[4] F. Feng, Y.M. Li, V. LeoreanuFotea, Application of level soft sets in##decision making based on intervalvalued fuzzy soft sets, Computers and##Mathematics with Applications 60 (2010) 17561767.##[5] F. Feng, Y.B. Jun, X.Y. Liu, L.F. Li, An adjustable approach to fuzzy##soft set based decision making, Journal of Computational and Applied##Mathematics 234 (2010) 1020.##[6] F. Feng, X.Y. Liu, V. LeoreanuFotea, Y.B. Jun, Soft sets and soft rough##sets, Information Sciences 181 (2011) 11251137.##[7] F. Feng, Y.M. Li, N. Cagman, Generalized uniint decision making##schemes based on choice value soft sets, European Journal of Operational##Research 220 (2012) 162170.##[8] D. Freni, {it Une note sur le cÂœur d'un hypergroupe et sur la cl^{o}ture transitive##$betasp ast$ de $beta$. (French) [A note on the core of a##hypergroup and the transitive closure $betasp ast$ of##$beta$]}, Riv. Mat. Pura Appl., 8 (1991) 153156.##[9] M. Koskas, Groupes et hypergroupes homomorphes a un##demihypergroupe, C. R. Acad Sc., Paris, 257 (1963), 334337.##bibitem{4}##[10] P.K. Maji, A.R. Roy, R. Biswas, An application of soft sets in a decision##making problem, Computers and Mathematics with Applications 44 (2002) 1077##[11] F. Marty, {it Sur une Generalization de la Notion de Groupe}, 8th Congress##Math. Scandenaves, Stockholm, Sweden, (1934) 4549.##[12] D. Molodtsov, Soft set theory first results, Comput. Math. Appl. 37 (1999) 19Â–31.##[13]T. Vougiouklis, {it Hyperstructures and Their Representations}, Hadronic##Press, Palm Harbor, FL, 1994.##]
Similarity DHAlgebras
2
2
In cite{GL}, B. Gerla and I. Leuc{s}tean introduced the notion of similarity on MValgebra. A similarity MValgebra is an MValgebra endowed with a binary operation $S$ that verifies certain additional properties. Also, Chirtec{s} in cite{C}, study the notion of similarity on L ukasiewiczMoisil algebras. In particular, strong similarity L ukasiewiczMoisil algebras were defined. In this paper we define and study the variety of similarity symmetric Heyting algebras (or similarity DHalgebras), i.e. symmetric Heyting algebras endowed with an operation of similarity $S$. These algebras are a generalization of strong similarity L ukasiewiczMoisil algebras. In addition, we introduce a propositional calculus and prove this calculus has similarity DHalgebras as algebraic counterpart.
1

59
71


Federico
Gabriel Alminana
Universidad Nacional de San Juan.
Universidad Nacional de San Juan.
Argentina


Mathias
Exequiel Pelayes
Universidad Nacional de San Juan.
Universidad Nacional de San Juan.
Argentina
symmetric Heyting algebras
Similarity
$S$filter
[[1] V. Boicescu, A. Filipoiu, G. Georgescu and S. Rudeanu, LukasiewiczMoisil Algebras, Anals of Discrete Mathematics, 49, NorthHolland, The Netherlands, 1991.##[2] J.L. Castro, F. Klawonn, Similarity in Fuzzy Reasoning, using Fuzzy Logic. Mathware and Soft Computing, 2:##197228, 1995.##[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, 331355.##[4] F. Chirtes, Similarity Lukasiewicz{Moisil algebras, An. Univ. Craiova Ser. Mat. Inform. 35 (2008), 5475.##[5] F. Formato, G. Gerla, M. Sessa, Similaritybased unication, Fundamenta Informaticae, 41: 393414, 2000.##[6] G. Georgescu, A. Popescu, Concept lattices and similarity in noncommutative fuzzy logic, Fundamenta Informaticae, 53: 2354, 2002.##[7] B. Gerla and I. Leustean, Similarity MV{algebras, Fund. Inform. 69 (2006), no. 3, 287300.##[8] A. Monteiro, Sur les algebres de Heyting Simetriques, Special issue in honor of Antonio Monteiro. Portugal. Math. 39(1{4), 1980.##[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) 242245.##[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, 5155.##[11] H.P. Sankappanavar, Heyting algebras with a dual lattice endomorphism, Z. Math. Logik Grundlag. Math. 33 (1987), no. 6, 565573.##[12] E. Turunen, A Lukasiewiczstyle manyvalued similarity reasoning. Review. in Beyond Two: Theory and Applications of Multiple Valued Logic, Melvin Fitting and Ewa Orlowska editors, 311321, 2003.##[13] L. Zadeh, Similarity relations and fuzzy orderings, Information Sciences, 3: 177200, 1971.##]