ORIGINAL_ARTICLE
Optimization of Iran’s Production in Forouzan Common Oil Filed based on Game Theory
One of Iran's problems in the production of common oil and gas fields is unequal extraction. Therefore, the production of common oil and gas fields in onshore and offshore is essential for Iran, so this must carefully monitor, which can be considered as a game-liked approach, that each player tries to increase its payoff. Therefore, the purpose of this study is to apply game theory in examining Iran's approaches to extracting from common oil fields. For this purpose, the present study seeks to design a mathematical model to optimize the production of Iran against a competitor using a game. Since the proposed model is in the field of mathematical modeling, the research strategy is a case study. Meanwhile, the data-gathering tool is descriptive. The results showed that Iran's equilibrium in Forouzan oil field is cooperation, and the equilibrium of Saudi Arabia is non-cooperation. Finally, the executive policies based on research results presented.
https://mir.kashanu.ac.ir/article_110785_a691e535eb3b708b6b52b18da4a3c5a3.pdf
2020-09-01
173
192
10.22052/mir.2020.238991.1222
Game Theory
Common Fields
Oil & Gas
Cooperative Game
Forouzan Oil Filed
Seyed Pendar
Toufighi
toufighi.p@ut.ac.ir
1
Faculty of Management, University of Tehran, Kish International Campus, I. R. Iran
LEAD_AUTHOR
Mohamadreza
Mehregan
mehregan@ut.ac.ir
2
Faculty of Management, University of Tehran, I. R. Iran
AUTHOR
Ahmad
Jafarnejad
jafarnjd@ut.ac.ir
3
Faculty of Management, University of Tehran, I. R. Iran
AUTHOR
[1] L. Argha (in Persian), Investigating the Sanctions on Iran’s Oil and Gas Section Using Game Theory, MSc Thesis, Tarbiat Modares University, 2011.
1
[2] E. Bayati, B. Safavi and A. Jafarzadeh (in Persian), Iran-Qatar cooperation in extracting common gas reserves of south pars (north dome) with emphasis on game theory, Q. J. Econ. Model. Res. 45 (1) (2019) 47 − 72.
2
[3] J. C. B. Cooper, Price elasticity of demand for crude oil: estimates for 23 countries, OPEC Rev. 27 (1) (2003) 1 − 8.
3
[4] S. Dosenrode, Federalism theory and neo-functionalism: elements for an analytical framework, Perspect. Fed. 2 (3) (2010) 1 − 28.
4
[5] A. Emami Meybodi, J. Kashani, G. Abdoli, A. Taklif and P. Fotouhi Mozafarian (in Persian), Review of Iran and Iraq strategies for exploitation of common oil fields, Quar. Ener. Eco. Rev. 15 (60) (2019) 24 − 50.
5
[6] M. Esmaeili, A. Bahrini and S. Shayanrad, Using game theory approach to interpret stable policies for Iran’s oil and gas common resource conflicts with Iraq and Qatar, Anim. Genet. 11 (4) (2015) 543 − 554.
6
[7] W. Gao, P. R. Hartley and R. C. Sickles, Optimal dynamic production from a large oil field in Saudi Arabia, Empir. Econ. 37 (2009) 153 − 184.
7
[8] A. Ghavam (in Persian), Principles of foreign policy and international policy, SAMT Org. Pub, Tehran, 2011.
8
[9] H. Hajiani (in Persian), Legal and contractual solutions for the exploitation of common oil and gas fields, New Sci. Approach Conf. Iran. Humanit. 2017.
9
[10] V. Havas, War of attrition in the Arctic offshore: Technology spillovers and risky investments in oil and gas extraction, MSc Thesis, University of Oslo, 2015.
10
[11] J. Kashani (in Persian), Legal status of oil and gas deposits across national frontiers, Law. Rev. 25 (39) (2009) 165 − 219.
11
[12] F. G. Lakkis, Where is the alloimmune response initiated?, Am. J. Transplant. 3 (3) (2003) 241 − 242.
12
[13] S. Lozano, P. Moreno, B. Adenso-Díaz, and E. Algaba, Cooperative game theory approach to allocating benefits of horizontal cooperation, Eur. J. Oper. Res. 229 (2) (2013) 444 − 452.
13
[14] A. Mirzaalian, M. Kermanshah and M. Moayedi (in Persian), Technical and legal approaches to the development of common oil and gas fields, Sci. Mon. Promot. Oil Gas Explor. Prod. 128 (2015) 19 − 23.
14
[15] T. Mohammadi and M. Motamedi (in Persian), Dynamic optimization of oil production in Iran (Case study of Haftgel oil field with emphasis on conservation production), Econ. Res. Rev. 10 (38) (2010) 235 − 265.
15
[16] A. Niemann and P. C. Schmitter, Neo-functionalism, in: A. Wiener and T. Diez (eds), Theories of European Integration, Oxford Univ. Press, 2nd Edition (2009) pp. 45 − 66.
16
[17] E. Nojomi and F. Darvishi (in Persian), Iran joint hydrocarbon reservoirs in the Persian Gulf region challenges and opportunities, geography, Sci. J. Geogr. Soc. Iran 5 (12-13) (2007) 167 − 186.
17
[18] S. Shahbazi and K. Soleimanian, Iran’s strategy in utilizing common resources of oil and gas: Game Theory Approach, Iran. J. Econ. Res. 6 (2) (2017) 185 − 202.
18
[19] M. Shalbaf and A. Maleki (in Persian), Best interaction policy in joint fields governance between states; the case of Iraq-Iranian joint fields, Public Policy 1 (4) (2016) 41 − 60.
19
[20] H. Zonnoor and S. Matin (in Persian), Optimal oil Production in Iran: A dynamic programming model, the Journal of Plan. Budg. 20 (4) (2016) 107−136.
20
ORIGINAL_ARTICLE
An ECDLP-Based Verifiable Multi-Secret Sharing Scheme
Secret sharing is an important issue in cryptography which has many applications. In a secret sharing scheme, a secret is shared by a dealer among several participants in such a way that any authorized subset of participants can recover the secret by pooling their shares. Recently, several schemes based on elliptic curves and bilinear maps have been presented. Some of these schemes need a secure channel, there are restrictions on the number of secrets, or the participants or the dealer are unable to verify the validity of the shares. In this paper, we present a new verifiable (t, n)-threshold multi-secret sharing scheme based on elliptic curves and pairings that does not have any of the above restrictions. The hardness of a discrete logarithm problem on elliptic curves guarantees the security of the proposed scheme.
https://mir.kashanu.ac.ir/article_110206_528cce9bdefe9ab0254a1538bdb78e2f.pdf
2020-09-01
193
206
10.22052/mir.2020.217418.1193
Secret Sharing Scheme
Elliptic Curves
Pairings
Discrete Logarithm Problem
Khadijeh
Eslami
kh.eslami@grad.kashanu.ad.ir
1
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, I. R. Iran
AUTHOR
Mojtaba
Bahramian
bahramianh@kashanu.ac.ir
2
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, I. R. Iran
LEAD_AUTHOR
[1] V. P. Binu and A. Sreekumar, Threshold Multi Secret Sharing Using Elliptic Curve and Pairing, Int. J. Inform. Process 9 (4) (2015) 100-112.
1
[2] G. Blakley, Safeguarding cryptographic keys, Proc AFIPS 1979 National Computer Conference, AFIPS Press, New york, 1979, pp. 313-317.
2
[3] W. Chen, X. Long, Y. B. Bai and X. P. Gao, A new dynamic threshold secret sharing scheme from bilinear maps, International Conference on Parallel Processing Workshops (ICPPW 2007), Xian, 2007, p. 19.
3
[4] B. Chor, S. Goldwasser, S. Micali and B. Awerbuch, Verifiable secret sharing and achieving simultaneity in the presence of faults [A], 26th Annual Symposium on Foundations of Computer Science (sfcs 1985), Portland, OR, USA, 1985, pp. 383-395, DOI: 10.1109/SFCS.1985.64.
4
[5] L. Harn, Efficient sharing (broadcasting) of multiple secret, in IEE Proceedings - Computers and Digital Techniques 142 (3) (1995) 237-240.
5
[6] N. Koblitz, Elliptic curve cryptosystems, Math. Comp. 48 (177) (1987) 203-209.
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[7] H. S. Lee, A self-pairing map and its applications to cryptography, Appl. Math. Comput. 151 (3) (2004) 671-678.
7
[8] D. Liu, D. Huang, P. Luo and Y. Dai, New schemes for sharing points on an elliptic curve, Comput. Math. Appl. 56 (6) (2008) 1556-1561.
8
[9] V. Miller, Use of elliptic curves in cryptography, Advances in cryptology-CRYPTO '85 (Santa Barbara, Calif., 1985), 417--426, Lecture Notes in Comput. Sci., 218, Springer, Berlin, 1986.
9
[10] N. Patel, P. D. Vyavahare and M. Panchal, A Novel Verifiable Multi-Secret Sharing Scheme Based on Elliptic Curve Cryptography, The Tenth International Conference on Emerging Security Information, Systems and Technologies, 2016.
10
[11] A. Shamir, How to share a secret, Comm. ACM 22 (11) (1979) 612-613.
11
[12] R. Shi, H. Zhong and L. Huang, A (a(t, n)-threshold verified multi-secret sharing scheme based on ecdlp, Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing (SNPD 2007), Qingdao, 2007, pp. 9--13, DOI:10.1109/SNPD.2007.416.
12
[13] C. Tang, D. Pei, Z. Liu and Y. He, Non-interactive and information theoretic secure publicly verifiable secret sharing, Cryptology ePrint Archive, Report 2004/201, 2004, (available at http://eprint.iacr.org/).
13
[14] S. J. Wang, Y. R. Tsai and C. C. Shen, Verifiable threshold scheme in multi-secret sharing distributions upon extensions of ecc, Wireless Pers. Commun. 56 (1) (2011) 173-182.
14
ORIGINAL_ARTICLE
New Criteria for Univalent, Starlike, Convex, and Close-to-Convex Functions on the Unit Disk
In the present paper, we introduce and investigate three interesting superclasses SD, SD* and KD of analytic, normalized and univalent functions in the open unit disk D. For functions belonging to these classes SD, SD* and KD, we derive several properties including (for example) the coefficient bounds and growth theorems. The various results presented here would generalize many well known results. We also get a new univalent criterion and some interesting properties for univalent function,starlike function,convex function and close-to-convex function. Many superclasses which are already studied by various researchers are obtained as special cases of our two new superclasses.
https://mir.kashanu.ac.ir/article_110783_30eb1d8766627bb78886aec4314e3c14.pdf
2020-09-01
207
223
10.22052/mir.2020.223553.1200
Univalent functions
starlike functions
Convex functions
Close-to-convex function
Mohammad Reza
Yasamian
myasamian@yahoo.com
1
Department of Mathematics, Payame Noor University, Tehran, Iran.
LEAD_AUTHOR
Ali
Ebadian
ebadian.ali@gmail.com
2
Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran
AUTHOR
Mohammad Reza
Foroutan
foroutan_mohammadreza@yahoo.com
3
Department of Mathematics, Payame Noor University, Tehran, Iran.
AUTHOR
[1] L. Bieberbach, Uber die Koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln, S. -B. Preuss. Akad. Wiss. 138 (1916) 940-955.
1
[2] P. L. Duren, Univalent Functions, Springer-Verlag, New York, 1983.
2
[3] I. Graham and G. Kohr, Geometric Function Theory in one and Higher Dimension, Marcel. Dekker, New York, 2003.
3
[4] T. H. Gronwall, Some remarks on conformal representation, Ann. Math. Ser. 2 16 (1914-1915) 72-76.
4
[5] J. A. Jenkins, Univalent Functions and Conformal Mapping, Erg. Math. Grenzgeb. 18, Springer-Verlag, Berlin-Gottingen-Heidelberg, 1958.
5
[6] O. Lehto, Univalent functions and Teichmuller Spaces, Springer-Verlag, New York, 1987.
6
[7] P. Koebe, Uber die Uniformisierung beliebiger analytischer Kurven, Nachr. Kgl. Ges. Wiss. Gottingen Math.-Phys. Kl. (1907) 191-210.
7
[8] D. K. Thomas, N. Tuneski and A. Vasudevarao, Univalent Functions: A Primer, Vol. 69. Walter de Gruyter GmbH & Co KG, Berlin, 2018.
8
ORIGINAL_ARTICLE
Numerical Solution of System of Nonlinear Integro-Differential Equations Using Hybrid of Legendre Polynomials and Block-Pulse Functions
In this paper, numerical techniques are presented for solving system of nonlinear integro-differential equations. The method is implemented by applying hybrid of Legendre polynomials and Block-Pulse functions. The operational matrix of integration and the integration of the cross product of two hybrid function vectors are derived in order to transform the system of nonlinear integro-differential equations into a system of algebraic equations. Finally, the accuracy of the method is illustrated through some numerical examples and the corresponding results are presented.
https://mir.kashanu.ac.ir/article_93285_452cc3ccf524375be3bfce057abbabf9.pdf
2020-09-01
225
238
10.22052/mir.2019.173293.1119
Integro-differential equations
Hybrid functions
Block-Pulse functions
Legendre polynomials
operational matrix
Mehdi
Sabzevari
sabzevari@kashanu.ac.ir
1
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
LEAD_AUTHOR
Fatemeh
Molaei
fatemehmolaie@ymail.com
2
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
AUTHOR
[1] J. Abdul, Introduction to Integral Equations with Applications, Wiley, New York, 1999.
1
[2] M. Alipour, D. Baleanu and F. Babaei, Hybrid Bernstein Block-Pulse functions method for second kind integral equations with convergence analysis, Abstr. Appl. Anal. 2014 (2014) 623763.
2
[3] R. Y. Chang and M. L. Wang, Shifted Legendre direct method for variational problems, J. Optim. Theory Appl. 39 (1983) 299 − 307.
3
[4] K. B. Datta and B. M. Mohan, Orthogonal Functions in Systems and Control, World Scientific, Singapore, 1995.
4
[5] S. M. Hashemiparast, M. Sabzevari and H. Fallahgoul, Improving the solution of nonlinear Volterra integral equations using rationalized Haar s-functions, Vietnam J. Math. 39 (2) (2011) 145 − 157.
5
[6] S. M. Hashemiparast, M. Sabzevari and H. Fallahgoul, Using crooked lines for the higher accuracy in system of integral equations, J. Appl. Math. Inform. 29 (2011) 145 − 159.
6
[7] S. M. Hashemiparast, H. Fallahgoul and A. Hosseyni, Fourier series approximation for periodic solution of system of integral equations using Szego-Bernstein weights, Int. J. Comput. Math. 87 (2010) 1485−1496.
7
[8] C. H. Hsiao, Hybrid function method for solving Fredholm and Volterra integral equations of the second kind, J. Comput. Appl. Math. 230 (2009) 59−68.
8
[9] M. Javidi, Modified homotopy perturbation method for solving system of linear Fredholm integral equations, Math. Comput. Modelling 50 (2009) 159−165.
9
[10] Z. Jiang and W. Schanfelberger, Block-Pulse Functions and their Applications in Control Systems, Springer-Verlag, Berlin, 1992.
10
[11] K. Maleknejad and M. Tavassoli Kajani, Solving second kind integral equations by Galerkin methods with hybrid Legendre and Block-Pulse functions, Appl. Math. Comput. 145 (2003) 623−629.
11
[12] K. Maleknejad, B. Basirat and E. Hashemzadeh, Hybrid Legendre polynomials and Block-Pulse functions approach for nonlinear Volterra-Fredholm integro-differential equations, Comput. Math. Appl. 61 (2011) 2821−2828.
12
[13] A. Saadatmandi and M. Dehghan, A Legendre collocation method for fractional integro-differential equations, J. Vib. Control 17 (2011) 2050−2058.
13
[14] M. Sabzevari, Erratum to "Numerical solution of linear Fredholm integral equation by using hybrid Taylor and Block-Pulse functions", Appl. Math. Comput. 339 (2018) 302−307.
14
[15] H. Sadeghi Goghari and M. Sadeghi Goghari, Two computational methods for solving linear Fredholm fuzzy integral equation of the second kind, Appl. Math. Comput. 182 (2006) 791 − 796.
15
[16] P. K. Sahu and S. S. Ray, Hybrid Legendre Block-Pulse functions for the numerical solutions of system of nonlinear Fredholm-Hammerstein integral equations, Appl. Math. Comput. 270 (2015) 871−878.
16
[17] M. Tavassoli Kajani and A. Hadi Vencheh, Solving second kind integral equations with Hybrid Chebyshev and Block-Pulse functions, Appl. Math. Comput. 163 (2005) 71 − 77.
17
[18] S. Yüzbaşi, N. Şahin and M. Sezer, Numerical solutions of systems of linear Fredholm integro-differential equations with Bessel polynomial bases, Comput. Math. Appl. 61 (2011) 3079 − 3096.
18
ORIGINAL_ARTICLE
The Projection Strategies of Gireh on the Iranian Historical Domes
The Gireh is an Islamic geometric pattern which is governed by mathematical rules and conforms to Euclidean surfaces with fixed densities. Since dome-shaped surfaces do not have a fixed density, it is difficult to make use of a structure like Gireh on these surfaces. There are, however, multiple domes which have been covered using Gireh, which can certainly be thought of a remarkable achievement by past architects. The aim of this paper is to discover and classify the strategies employed to spread the Gireh over dome surfaces found in Iran. The result of this research can provide new insights into how Iranian architects of the past were able to extend the use of the Gireh from flat surfaces to dome-shaped elements. The result of this paper reveal that the projection of Gireh on dome surface is based on the following six strategies: 1- Spherical solids, 2- radial gore segments, 3- articulation, 4- changing Gireh without articulating, 5- changing the number of Points in the Gireh based on numerical sequences, and 6- hybrid. Except for the first method, all of the other strategies have been discovered in this study. The radial gore segments strategy is different from the previously-developed methods.
https://mir.kashanu.ac.ir/article_110812_68f9e0bb865ae60c9f2ec4795e516f98.pdf
2020-09-01
239
257
10.22052/mir.2020.212903.1187
Islamic mathematics
Geometry
Gireh
domical surface
pattern projection
Ahad
Nejad Ebrahimi
ahadebrahimi@tabriziau.ac.ir
1
Faculty of Architecture and urbanism, Tabriz Islamic Art University, Tabriz, Iran
LEAD_AUTHOR
Aref
Azizipour Shoubi
a.azizpour@tabriziau.ac.ir
2
Faculty of Architecture and urbanism, Tabriz Islamic Art University, Tabriz, Iran
AUTHOR
[1] S. J. Abas and A. S. Salman, Symmetries of Islamic Geometrical Patterns, New Jersey: World Scientific, Singapore, 1995.
1
[2]Y. Abdullahi and M. R. B. Embi, Evolution of Islamic geometric patterns, Front. Archit. Res. 2 (2) (2013) 243-251. DOI:10.1016/j.foar.2013.03.002
2
[3] R. Ajlouni, A seed-based structural model for constructing rhombic quasilattice with 7-fold symmetry, Struc. Chem. 29 (2018) 1875 - 1883. DOI:10.1007/s11224-018-1169-2
3
[4] R. Besenval, Technologie de la Vouˇte dans l’Orient Ancien, Editions Recherche sur les civilisations, Paris, 1984.
4
[5] J. Bonner, Doing the Jitterbug with Islamic geometric patterns, J. Math. Arts. 3 (12) (2018) 128-143. DOI:10.1080/17513472.2018.1466431
5
[6] J. Bonner, Islamic Geometric Patterns, Springer, New York, 2017.
6
[7] J. Bonner, The historical significance of the geometric designs in the northeast dome chamber of the Friday Mosque at Isfahan, Nexus Netw J. 18 (2016) 55-103. DOI: 10.1007/s00004-015-0275-3
7
[8] E. Broug, Islamic Geometric Design, Thames & Hudson, London, 2013.
8
[9] A-W. Buzjani, Hindisah Irani: K¯arbud-e Hindisah dar ‘Amal (Applied Geometry), trans by A jazbi, Soroush, Tehran, 1997. (In Persian)
9
[10] K. Critchlow, Islamic Patterns:An Analytical and Cosmological Approach, Thames & Hudson Ltd, London, 1984.
10
[11] M. P. do Carmo, Differential Geometry of Curves and Surfaces: Revised and Updated, Second Edition, Dover Publications Inc, New York, 2016.
11
[12] I. El-Said and A. Parman, Geometric Concepts in Islamic Art, Dale Seymour Pubn, Portland, 1989.
12
[13] A. N. Farabi, Ihs¯a Al-ul¯um, trans. H. Khadivjam, Tehran: Elmi va Farhangi Publications, 2002. (In Persian)
13
[14] M. J. Greenberg, Euclidean and Non-Euclidean Geometries: Development and History, W. H. Freeman, New York, 2008.
14
[15] E. H. Hankin, The Drawing of Ggeometric Patterns in Saracenic Art, Archaeological Survey of India, New Delhi, 1925.
15
[16] S. A. Hely, Gireh and Arch in Islamic Architecture, Hely, Kashan, 1986. (In Persian)
16
[17] C. E. Horne, Geometric Symmetry in Patterns and Tilings, Woodhead Publishing, Sawston, 2000.
17
[18] C. S. Kaplan and D. H. Salesin, Islamic star patterns in absolute geometry, ACM Trans. Graph. 23 (2) (2004) 97-119. DOI:10.1080/00210860802246184
18
[19] M. H. Kasraei, Y. Nourian and M. Mahdavinejad, Girih for domes: Analysis of three Iranian domes, Nexus Netw. J. 14 (2016) 311-321. DOI:10.1007/s00004-015-0282-4
19
[20] H. Lorzadeh, Ehya-ye Honar Ha-ye Az Yad Rafteh (Revival of Forgotten Arts), Molavi, Tehran, 2014. (In Persian)
20
[21] K. Navai and K. Haji Qassemi, Khesht-o Khial; An Interpretation of Iranian Islamic Architecture, Soroush, Tehran, 2011. (In Persian)
21
[22] G. Necipoğlu and M. Al-Asad, The Topkap scroll: geometry and ornament in Islamic architecture: Topkap palace museum library MS.Getty Center for the History of Art and the Humanities, Santa Monica, CA, 1995.
22
[23] A. Nejad Ebrahimi and A. Azizpour Shoubi, Gireh in Iranian domes; A case study of Hakim Mosque, Memari Shenasi 10 (2019) 1-6. (In Persian)
23
[24] A. Nejad Ebrahimi and A. Azizpour Shoubi, Identify domes with gireh in Iranian Mosques, Green Architecture 2 (15) (2019) 45-53. (In Persian)
24
[25] A. Özdural, A mathematical Sonata for architecture: Omar Khayyam and the Friday Mosque of Isfahan, Technology Culture 39 (4) (1998) 699-715.
25
[26] P. Paufler, B. Gr unbaum and G. C. Shephard, Tilings and Patterns, W. H. Freeman and Co. Ltd., Oxford, 1987.
26
[27] R. Sarhangi, Illustrating Abu al-Wafa’ Buzjani: Flat images, spherical constructions, Iran Studies 41 (2008) 511-523. (In Persian) DOI:10.1080/00210860802246184
27
[28] R. Sarhangi, Interlocking star polygons in persian architecture: The special case of the decagram in mosaic designs, Nexus Netw. J. 14 (2012) 345-372. DOI: 10.1007/s00004-012-0117-5
28
[29] A. Sharbaf, Gireh and Karbandi, Cultural Heritage Organization, Tehran, 2006. (In Persian)
29
[30] M. Raeisi, M. Bemanian and F. Tehrani, Rethinking the concept of karbandi based on theoretical geometry, practical geometry and building function, Maremat & Me’mari-e Iran 3 (2013) 33-54. (In Persian)
30
[31] H. Zumarshidi, Gireh Work in Islamic Architecture and Handicrafts, University Publication Center, Tehran, 1986. (In Persian)
31
ORIGINAL_ARTICLE
Some Results on the Strong Roman Domination Number of Graphs
Let G=(V,E) be a finite and simple graph of order n and maximum degree Δ(G). A strong Roman dominating function on a graph G is a function f:V (G)→{0, 1,… ,[Δ(G)/2 ]+ 1} satisfying the condition that every vertex v for which f(v)=0 is adjacent to at least one vertex u for which f(u) ≤ 1+ [(1/2)| N(u) ∩ V0| ], where V0={v ∊ V | f(v)=0}. The minimum of the values ∑v∊ V f(v), taken over all strong Roman dominating functions f of G, is called the strong Roman domination number of G and is denoted by γStR(G). In this paper we continue the study of strong Roman domination number in graphs. In particular, we present some sharp bounds for γStR(G) and we determine the strong Roman domination number of some graphs.
https://mir.kashanu.ac.ir/article_110816_2ff1aa058881fe3c1ad101ed2efb2b99.pdf
2020-09-01
259
277
10.22052/mir.2020.225635.1205
Domination
Roman domination
Roman domination number
strong Roman domination
Akram
Mahmoodi
ak.mahmoodi@pnu.ac.ir
1
Department of Mathematics, Payame Noor University, I. R. Iran
LEAD_AUTHOR
Sakineh
Nazari-Moghaddam
sakine.nazari.m@gmail.com
2
Department of Mathematics, Dehloran Branch, University of Applied Science and Technology Dehloran, I. R. Iran
AUTHOR
Afshin
Behmaram
behmarammath@gmail.com
3
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, I. R. Iran
AUTHOR
[1] M. P. Álvarez-Ruiz, I. González Yero, T. Mediavilla-Gradolph, S. M. Sheikholeslami and J. C. Valenzuela-Tripodoro, On the Strong Roman Domination Number of Graphs, Discrete Applied Math. 231 (2017) 44 - 59.
1
[2] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, American Elsevier, New York, 1976.
2
[3] E. W. Chambers, B. Kinnersley, N. Prince and D. B. West, Extremal problems for Roman domination, J. Discrete Math. 23 (2009) 1575 - 1586.
3
[4] C. S. Revelle and K. E. Rosing, Defendens imperium romanum: a classical problem in military strategy, Amer. Math. Monthly 107 (7) (2000) 585-594.
4
[5] I. Stewart, Defend the Roman Empire, Sci. Amer. 281 (6) (1999) 136 - 139.
5