2018
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Generation of High Efficient QuasiSingleCycle 3 and 6THZ Pulses using Multilayer Structures OH1/SiO2 and DSTMS/SiO2
2
2
We propose that high efficient terahertz (THz) multilayer structures are composed of DSTMS/SiO2 and OH1/SiO2 at 3 and 6THz frequencies. We show that the efficiencies of these structures are higher than DAST/SiO2 structure in both of 3 and 6THz frequencies. OH1/SiO2 structure at 6THz has an efficiency as large as 101; at 3THz frequency, DSTMS/SiO2 structure has an efficiency as large as 102. Meanwhile bulk OH1 has an efficiency as large as 103 at 3THz due to perfect phase matching whose efficiency is lower than DSTMS/SiO2 structure. We also show that other structures, namely DSTMS/ZnTe at 3THz and DAST/GaP at 8THz, have low efficiency, so they are not suitable as THz sources.
1

1
13


Hamid Reza
Zangeneh
Department of Photonics, Faculty of Physics, University of Kashan, Kashan, I. R. Iran
Department of Photonics, Faculty of Physics,
I R Iran
hrzangeneh@kashanu.ac.ir


Maryam
Kashani
Department of Photonics, Faculty of Physics, University of Kashan, Kashan, I. R. Iran
Department of Photonics, Faculty of Physics,
I R Iran
mkashani@grad.kashanu.ac.ir
Terahertz waves (THz)
Difference frequency generation (DFG)
Nonlinear susceptibility
Multilayer structure
Organic crystals.
[1. F. D. J. Brunner, O. P. Kwon, S. J. Kwon, M. Jazbinsek, A. Schneider, P. Günter, A hydrogenbonded organic nonlinear optical crystal for highefficiency terahertz generation and detection, Opt. Express 16 (2008) 16496– 16508.##2. F. D. J. Brunner, Generation and Detection of Terahertz Pulses in the Organic Crystals OH1 and COANP, a dissertation submitted to ETH Zurich, for the degree of Doctor of Sciences, 2009.##3. P. D. Cunningham, L. M. Hayden, Optical properties of DAST in the THz range, Opt. Express 18 (2010) 23620–23625.##4. C. Hunziker, S. J. Kwon, H. Figi, F. Juvalta, O. P. Kwon, M. Jazbinsek, P. Günter, Configurationally locked, phenolic polyene organic crystal 2 f3(4hydroxystyryl) 5,5dimethylcyclohex2enylidenegmalononitrile: linear and nonlinear optical properties, J. Opt. Soc. Am. B 25 (2008) 1678–1683.##5. O. P. Kwon, M. Jazbinsek, J. I. Seo, P. J. Kim, H. Yun, Y. S. Lee, P. Gunter, Optical nonlinearities and molecular conformations in Thiophenebased hydrazone crystals, J. Phys. Chem. C 113 (2009) 15405–15411.##6. Y. S. Lee, Principles of Terahertz Science and Technology, SpringerVerlag US, New York, 2009.##7. L. Mutter, F. D. J. Brunner, Z. Yang, M. Jazbinšek, P. Günter, Linear and nonlinear optical properties of the organic crystal DSTMS, J. Opt. Soc. Am. B 24 (2007) 2556–2561.##8. A. G. Stepanov, L. Bonacina, J. P. Wolf, DAST=SiO2 multilayer structure for efficient generation of 6 THz quasisinglecycle electromagnetic pulses, Opt. Lett. 37 (2012) 2439–2441.##9. A. G. Stepanov, A. Rogov, L. Bonacina, J. P. Wolf, C. P. Hauri, Tailoring singlecycle electromagnetic pulses in the 29 THz frequency range using DAST=SiO2 multilayer structures pumped at Ti:sapphire wavelength, Opt. Express 22 (2014) 21618–21625.##10. A. G. Stepanov, C. Ruchert, J. Levallois, C. Erny, C. P. Hauri, Generation of broadband THz pulses in organic crystal OH1 at room temperature and 10K, Opt. Mater. Express 4 (2014) 870–875.##11. M. Stillhart, A. Schneider, P. Günter, Optical properties of 4N, Ndimethylamino4’N’methylstilbazolium 2, 4, 6 trimethylbenzenesulfonate crystals at terahertz frequencies, J. Opt. Soc. Am. B 25 (2008) 1914–1919.##12. T. Tanabe, K. Suto, J. I. Nishizawa, K. Saito, T. Kimura, Frequencytunable terahertz wave generation via excitation of phononpolaritons in GaP, J. Phys. D: Appl. Phys. 36 (2003) 953–957.##13. C. Vicario, M. Jazbinsek, A. V. Ovchinnikov, O. V. Chefonov, S. I. Ashitkov, M. B. Agranat, C. P. Hauri, High efficiency THz generation in DSTMS, DAST and OH1 pumped by Cr:forsterite laser, Opt. Express 23 (2015) 4573–4580.##14. Z. Yang, L. Mutter, M. Stillhart, B. Ruiz, S. Aravazhi, M. Jazbinsek, A. Schneider, V. Gramlich, P. Günter, Largesize bulk and thinfilm stilbazoliumsalt single crystals for nonlinear optics and THz generation, Adv. Funct. Mater. 17 (2007) 20182023.##]
Fixed Point Theorems for kg Contractive Mappings in a Complete Strong Fuzzy Metric Space
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2
In this paper, we introduce a new class of contractive mappings in a fuzzy metric space and we present fixed point results for this class of maps.
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15
29


Kandala Kanakamahalakshmi
Sarma
Mathematics, College Of Science and Technology Andhra University, Visakhapatnam, Andhra Pradesh, India
Mathematics, College Of Science and Technology
India
sarmakmkandala@yahoo.in


Yohannes
Aemro
Mathematics, College of Science and Technology, Andhra University
Mathematics, College of Science and Technology,
India
yohannesgebru2005@gmail.com
Fixed points
strong fuzzy metric space
generalized kg  contractive mappings
[1. A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64(3) (1994) 395–399.##2. M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems 27(3) (1988) 385–389.##3. V. Gregori, S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets and Systems 115(3) (2000) 485–489.##4. V. Gregori, A. Sapena, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems Vol. 125, Issue 2, 2002, 245–252.##5. V. Gregori, A. Sapena, Remarks to “On strong intuitionistic fuzzy metrics", submitted to J. Nonlinear Sci. Appl..##6. J. Gutiérrez García, S. Romaguera, Examples of nonstrong fuzzy metrics, Fuzzy Sets and Systems 162(1)(2011) 91–93.##7. I. Kramosil, J. Michálek, Fuzzy metric and statistical metric spaces, Kybernetika 11(5) (1975) 336–344.##8. D. Miheţ, A class of contractions in fuzzy metric spaces, Fuzzy Sets and Systems 161(8) (2010) 1131–1137.##9. S. Phiangsungnoen, Y. J. Cho, P. Kumam, Fixed point results for modified various contractions in fuzzy metric spaces via αadmissible, Filomat 30(7) (2016) 1869–1881.##10. J. RodríguezLópez, S. Romaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy Sets and Systems 147(2) (2004) 273–283.##11. A. Sapena, S. Morillas, On strong fuzzy metrics, In: Proceedings of the Workshop in Applied Topology WiAT’09 (2009) 135–141.##12. B. Schweizer, A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960) 313–334.##13. S. L. Singh, R. Kamal, M. De la Sen, R. Chugh, A fixed point theorem for generalized weak contractions, Filomat 29(7) (2015) 1481–1490.##]
On Powers of Some Graph Operations
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2
Let $G*H$ be the product $*$ of $G$ and $H$. In this paper we determine the rth power of the graph $G*H$ in terms of $G^r, H^r$ and $G^r*H^r$, when $*$ is the join, Cartesian, symmetric difference, disjunctive, composition, skew and corona product. Then we solve the equation $(G*H)^r=G^r*H^r$. We also compute the Wiener index and Wiener polarity index of the skew product.
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31
43


Mohamed
Seoud
Department of Mathematics, Faculty of Science, Ain Shams University, Abbassia, Cairo, Egypt
Department of Mathematics, Faculty of Science,
Egypt
m.a.seoud@hotmail.com


Hamdy
Mohamed Hafez
Department of Basic science, Faculty of Computers and Information, Fayoum University, Fayoum 63514, Egypt
Department of Basic science, Faculty of Computers
Egypt
hha00@fayoum.edu.eg
Graph product
power graphs
graph indices
[1. R. Hammack, W. Imrich, S. Klavžar, Handbook of Product Graphs, CRC press, Boca Raton, FL, 2011.##2. F. Harary, Graph Theory, AddisonWesley Publishing Co., Reading, Mass. Menlo Park, Calif. London 1969.##3. F. Harary, G. W. Wilcox, Boolean operations on graphs, Math. Scand. 26(1) (1967) 41–51.##4. J. Ma, Y. Shi, J. Yue, The Wiener polarity index of graph products, Ars Combin. 116 (2014) 235–244.##5. S. Moradi, A note on tensor product of graphs, Iran. J. Math. Sci. Inform. 7(1) (2012) 73–81.##6. I. Peterina, P. Z. Pleteršek, Wiener index of strong product of graphs, Opuscula Math. 38(1) (2018) 81–94.##7. M. A. Seoud, On square graphs, Proc. Pakistan Acad. Sci. 25(1) (1991) 35–42.##8. M. A. Seoud, Operations related to squaring of graphs, Proc. Pakistan Acad. Sci. 28(3) (1991) 303–309.##9. M. A. Seoud, On power graphs, Ain Shams Science Bulletin 29(A) (1992) 125–135.##10. Y. Shibata, Y. Kikuchi, Graph products based on the distance in graphs, IEICE Trans. Fundamentals E83A(3) (2000) 459464.##11. H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69(1) (1947) 17–20.##12. Y. N. Yeh, I. Gutman, On the sum of all distances in composite graphs, Discrete Math. 135(13) (1994) 359–365.##]
Average DegreeEccentricity Energy of Graphs
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2
The concept of average degreeeccentricity matrix ADE(G) of a connected graph $G$ is introduced. Some coefficients of the characteristic polynomial of ADE(G) are obtained, as well as a bound for the eigenvalues of ADE(G). We also introduce the average degreeeccentricity graph energy and establish bounds for it.
1

45
54


Ivan
Gutman
University Kragujevac, Serbia
University Kragujevac, Serbia
Iran
gutman@kg.ac.rs


Veena
Mathad
Department of Mathematics
University of Mysore
Mysuru, India
Department of Mathematics
University of Mysore
Mys
India
veena_mathad@rediffmail.com


Shadi
Khalaf
Department of Studies in Mathematics, Faculty of Science and Technology Manasagangotri, University of Mysore, Mysore, India.
Department of Studies in Mathematics, Faculty
India
shadikhalaf1989@hotmail.com


Sultan
Mahde
Department of Mathematics
University of Mysore
Mysuru, India
Department of Mathematics
University of Mysore
Mys
India
sultan.mahde@gmail.com
Average degreeeccentricity matrix
average degreeeccentricity eigenvalue
average degreeeccentricity energy
[1. C. Adiga, M. Smitha, On maximum degree energy of a graph, Int. J. Contemp. Math. Sci. 4 (2009) 385–396.##2. R. Balakrishnan, The energy of a graph, Linear Algebra Appl. 387 (2004) 287–295.##3. H. E. Bell, Gerschgorin’s theorem and the zeros of polynomials, Am. Math. Monthly 72 (1965) 292–295.##4. D. J. H. Garling, Inequalities – A Journey Into Linear Analysis, Cambridge Univ. Press, Cambridge, 2007.##5. I. Gutman, The energy of a graph, Ber. Math.–Statist. Sekt. Forsch. Graz 103 (1978) 1–22.##6. I. Gutman, B. Furtula, Survey of graph energies, Math. Interdisc. Res. 2 (2017) 85–129.##7. I. Gutman, B. Furtula, The total Pielectron energy saga, Croat. Chem. Acta 90 (2017) 359–368.##8. F. Harary, Graph Theory, Addison Wesley, Reading, 1969.##9. N. Jafari Rad, A. Jahanbani, I. Gutman, Zagreb energy and Zagreb Estrada index of graphs, MATCH Commun. Math. Comput. Chem. 79 (2018) 371–386.##10. X. Li, Y. Shi, I. Gutman, Graph Energy, Springer, New York, 2012.##11. V. Mathad, S. S. Mahde, The minimum hub energy of a graph, Palest. J. Math. 6 (2017) 247–256.##12. B. J. McClelland, Properties of the latent roots of a matrix: The estimation of pielectron energies, J. Chem. Phys. 54 (1971) 640–643.##13. M. A. Naji, N. D. Soner, The maximum eccentricity energy of a graph, Int. J. Sci. Engin. Res. 7 (2016) 5–13.##14. H. S. Ramane, I. Gutman, J. B. Patil, R. B. Jummannaver, Seidel signless Laplacian energy of graphs, Math. Interdisc. Res. 2 (2017) 181–192.##15. D. S. Revankar, M. M. Patil, H. S. Ramane, On eccentricity sum eigenvalue and eccentricity sum energy of a graph, Ann. Pure Appl. Math. 13 (2017) 125–130.##16. B. Sharada, M. I. Sowaity, I. Gutman, Laplacian sumeccentricity energy of a graph, Math. Interdisc. Res. 2 (2017) 209–219.##17. M. I. Sowaity, B. Sharada, The sumeccentricity energy of a graph, Int. J. Rec. Innovat. Trends Comput. Commun. 5 (2017) 293–304.##]
Some Applications of Strong Product
2
2
Let G and H be graphs. The strong product GH of graphs G and H is the graph with vertex set V(G)V(H) and u=(u1, v1) is adjacent with v= (u2, v2) whenever (v1 = v2 and u1 is adjacent with u2) or (u1 = u2 and v1 is adjacent with v2) or (u1 is adjacent with u2 and v1 is adjacent with v2). In this paper, we ﬁrst collect the earlier results about strong product and then we present applications of these results in working with some important graphs such as Fence graphs.
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55
65


Mostafa
Tavakoli
Department of Applied Mathematics
Ferdowsi University of Mashhad
P. O. Box 1159, Mashhad 91775, I. R. Iran
Department of Applied Mathematics
Ferdowsi
I R Iran
m_tavakoli@um.ac.ir


Freydoon
Rahbarnia
Department of Applied Mathematics
Ferdowsi University of Mashhad
P. O. Box 1159, Mashhad 91775, I. R. Iran
Department of Applied Mathematics
Ferdowsi
I R Iran
rahbarnia@um.ac.ir


Irandokht
Rezaee Abdolhosein Zadeh
Department of Applied Mathematics
Ferdowsi University of Mashhad
P. O. Box 1159, Mashhad 91775, I. R. Iran
Department of Applied Mathematics
Ferdowsi
I R Iran
ir_rezaee899@stu.um.ac.ir
strong product
graph invariant
topological index
[1. A. R. Ashrafi, T. Došlić, A. Hamzeh, Extremal graphs with respect to the Zagreb coindices, MATCH Commun. Math. Comput. Chem. 65(1) (2011) 85–92.##2. A. R. Ashrafi, T. Došlić, M. Saheli, The eccentric connectivity index of TUC4C8(R) nanotubes, MATCH Commun. Math. Comput. Chem. 65(1) (2011) 221–230.##3. A. R. Ashrafi, M. Saheli, M. Ghorbani, The eccentric connectivity index of nanotubes and nanotori, J. Comput. Appl. Math. 235 (2011) 4561–4566.##4. G. G. Cash, Polynomial expressions for the hyperWiener index of extended hydrocarbon networks, Comput. Chem. 25 (2001) 577–582.##5. G. G. Cash, Relationship between the Hosoya polynomial and the hyperWiener index, Appl. Math. Lett. 15 (2002) 893–895.##6. A. A. Dobrymin, R. Entringer, I. Gutman, Wiener index of trees: theory and applications, Acta Appl. Math. 66 (2001) 211–249.##7. A. A. Dobrymin, I. Gutman, S. Klavšar, P. Žigert, Wiener index of hexagonal systems, Acta Appl. Math. 72 (2002) 247–294.##8. S. Gupta, M. Singh, A. K. Madan, Eccentric distance sum: a novel graph invariant for predicting biological and physical properties, J. Math. Anal. Appl. 275 (2002) 386–401.##9. I. Gutman, Relation between hyperWiener and Wiener index, Chem. Phys. Lett. 364 (2002) 352–356.##10. I. Gutman, N. Trinajstić, Graph theory and molecular orbitals. Total ф electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535–538.##11. R. Hammack, W. Imrich, S. Klavšar, Handbook of Product Graphs, Second edition, CRC Press, Boca Raton, FL, (2011).##12. H. Hosoya, Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons, Bull. Chem. Soc. Jpn. 44 (1971) 2332–2339.##13. A. Ilić, I. Gutman, Eccentric connectivity index of chemical trees, MATCH Commun. Math. Comput. Chem. 65 (2011) 731–744.##14. M. H. Khalifeh, H. YousefiAzari, A. R. Ashrafi, The hyperWiener index of graph operations, Comput. Math. Appl. 56 (2008) 1402–1407.##15. S. Klavšar, P. Žigert, I. Gutman, An algorithm for the calculation of the hyperWiener index of benzenoid hydrocarbons, Comput. Chem. 24 (2000) 229–233.##16. D. J. Klein, I. Lukovits, I. Gutman, On the definition of the hyperWiener index for cyclecontaining structures, J. Chem. Inf. Comput. Sci. 35 (1995) 50–52.##17. M. J. Morgan, S. Mukwembi, H. C. Swart, On the eccentric connectivity index of a graph, Discrete Math. 311 (2011) 1229–1234.##18. B. E. Sagan, Y. N. Yeh, P. Zhang, The Wiener polynomial of a graph, Int. J. Quant. Chem. 60(5) (1996) 959–969.##19. V. Sharma, R. Goswami, A. K. Madan, Eccentric connectivity index: a novel highly discriminating topological descriptor for structure property and structure activity studies, J. Chem. Inf. Comput. Sci. 37 (1997) 273–282.##20. M. Tavakoli, F. Rahbarnia, A. R. Ashrafi, Note on strong product of graphs, Kragujevac J. Math. 37(1) (2013) 187–193.##21. H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947) 17–20.##22. G. Yu, L. Feng, A. Ilić, On the eccentric distance sum of trees and unicyclic graphs, J. Math. Anal. Appl. 375 (2011) 99–107.##23. B. Zhou, Zagreb indices, MATCH Commun. Math. Comput. Chem. 52 (2004) 113–118.##24. B. Zhou, Z. Du, On eccentric connectivity index, MATCH Commun. Math. Comput. Chem. 63 (2010) 181–198.##25. B. Zhou, I. Gutman, Relations between Wiener, hyperWiener and Zagreb indices, Chem. Phys. Lett. 394 (2004) 93–95.##]
On EdgeDecomposition of Cubic Graphs into Copies of the DoubleStar with Four Edges
2
2
A tree containing exactly two nonpendant vertices is called a doublestar. Let $k_1$ and $k_2$ be two positive integers. The doublestar with degree sequence $(k_1+1, k_2+1, 1, ldots, 1)$ is denoted by $S_{k_1, k_2}$. It is known that a cubic graph has an $S_{1,1}$decomposition if and only if it contains a perfect matching. In this paper, we study the $S_{1,2}$decomposition of cubic graphs. We present some necessary and some sufficient conditions for the existence of an $S_{1, 2}$decomposition in cubic graphs.
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Abbas
Seify
Department of Sciences,
Shahid Rajaei Teacher Training University,
Tehran, I. R. Iran
Department of Sciences,
Shahid Rajaei Teacher
I R Iran
abbas.seify@gmail.com
Edgedecomposition
doublestar
cubic graph
regular graph
bipartite graph
[1. J. Barát, D. Gerbner, Edgedecomposition of graphs into copies of a tree with four edges, Electron. J. Combin. 21(1) (2014) Paper 1.55, 11 pp.##2. J. Bensmail, A. Harutyunyan, T. N. Le, M. Merker, S. Thomassé, A Proof of the BarátThomassen Conjecture, arXiv:1603.00197.##3. A. Bondy, U. S. R. Murty, Graph Theory, Graduate Texts in Mathematics, Springer, New York, (2008).##4. A. Kötzig, Aus der theorie der endlichen regulären graphen dritten und vierten grades, Časopis. Pěst. Mat. 82 (1957) 76–92.##5. C. Thomassen, Edgedecompositions of highly connected graphs into paths, Abh. Math. Semin. Univ. Hambg. 78 (2008) 17–26.##6. C. Thomassen, Decompositions of highly connected graphs into paths of length 3, J. Graph Theory 58 (2008) 286–292.##]