On enumeration of labeled connected transitive digraphs
*Khalid Sh. Al’DzhabriCorresponding authorkhalid.aljabrimath@qu.edu.iqDepartment of Mathematics College of Education University of Al Qadisiyah Department οf Mathematics University οf Al-Qadisiyah Cοllege οf EducatiοnAl Diwaniyah, 58002, Iraq0000-0003-4237-2366View full profile → , V. I. Rodionovrodionov@uni.udm.ruDepartment of Informatics and Mathematics Udmurt State UniversityIzhevsk, RussiaView full profile →
* Corresponding author · click or hover a name for details
- Published Online:
- 08 Sep 2023
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1631
- Pages:
- 1329–1340
Abstract
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References
[1] N.P. Adamenko and I.G. Velichko. Classification of topologies on finite sets using graphs. Ukrainian Mathematical Journal, 60(7) : 1164-1167 (2008). https://doi.org/10.1007/s11253-008-0113-9.
[2] Kh.Sh. Al’Dzhabri and V.I. Rodionov. The graph of partial orders. Vestn. Udmurt. Univ., Mat. Mekh. Komp’yut. Nauki, 4 : 3-12 (2013). https://doi.org/10.20537/vm130401.
[3] Kh.Sh. Al’Dzhabri. The graph of reflexive-transitive relations and the graph of finite topologies. Vestn. Udmurt. Univ., Mat. Mekh. Komp’yut. Nauki, 25(1) : 3-11 (2015). https://doi.org/10.20537/vm150101.
[4] Kh.Sh. Al’Dzhabri and V.I. Rodionov. The graph of acyclic digraphs. Vestn. Udmurt. Univ., Mat. Mekh. Komp’yut. Nauki, 25(4) : 441-452 (2015). https://doi.org/10.20537/vm150401.
[5] Kh.Sh. Al’Dzhabri and V.I. Rodionov. On support sets of acyclic and transitive digraphs. Vestn. Udmurt. Univ., Mat. Mekh. Komp’yut. Nauki, 27(2) : 153-161 (2017). https://doi.org/10.20537/vm170201.
[6] Z.I. Borevich. Enumeration of finite topologies, J. Sov. Math., 20(6):2532-2545 (1982) https://doi.org/10.1007/BF01681470.
[7] Z.I. Borevich, W. Wieslaw, E. Dobrowolski and V.I. Rodionov. The number of labeled topologies on nine points. J. Sov. Math., 37(2) : 937-942 (1987). https://doi.org/10.1007/BF01089085.
[8] Z.I. Borevich, V.V. Bumagin and V.I. Rodionov. Number of labeled topologies on ten points. J. Sov. Math., 17(4) : 1941-1945 (1981). https://doi.org/10.1007/BF01465449.
[9] G. Brinkmann and B. D. McKay. Posets on up to 16 points. Order, 19(2) : 147-179 (2002). https://doi.org/10.1023/A:1016543307592.
[10] L. Comtet. Recouvrements, bases de filtre et topologies d’un ensemble fini. C. R. Acad. Sci., 262 : A1091-A1094 (1966).
[11] S. K. Das. A machine representation of finite topologies. J. Assoc. Comput. Mach., 24(4) : 676-692 (1977). https://doi.org/10.1145/322033.322045.
[12] M. Erne. Struktur- und anzahlformeln fur topologien auf endlichen mengen. Manuscripta Math., 11 : 221-259 (1974). https://doi.org/10.1007/ BF01173716.
[13] M. Erne and K. Stege. Counting finite posets and topologies. Order, 8(3) : 247-265 (1991). https://doi.org/10.1007/BF00383446.
[14] J.W. Evans, F. Harary and M.S. Lynn. On the computer enumeration of finite topologies. Comm. ACM, 10(5) : 295-297 (1967). https://doi.org/10.1145/ 363282.363311.
[15] W. Gao and M.R. Farahani. The Zagreb topological indices for a type of Benzenoid systems jagged-rectangle. Journal of Interdisciplinary Mathematics, 20(5) : 1341-1348 (2017). https://doi.org/10.1080/09720502.2016.1232037.
[16] M. Imran, A.A.E. Abunamous, D. Adi, S.H. Rafique, A.Q. Baig and M.R. Farahani. Eccentricity based topological indices of honeycomb networks. Journal of Discrete Mathematical Sciences and Cryptography, 22(7) : 1199-1213 (2019). https://doi.org/10.1080/09720529.2019.1691326.
[17] M. Imran, M.K. Siddiqui, S. Ahmad, M.F. Hanif, M.H. Muhammad and M.R. Farahani. Topological properties of Benzenoid, phenylenes and nanostar dendrimers. Journal of Discrete Mathematical Sciences and Cryptography, 22(7):1229-1248 (2019). https://doi.org/10.1080/09720529.2019.1701267.
[18] A.J.M. Khalaf, S. Hussain, D. Afzal, F. Afzal and A. Maqbool. M-Polynomial and topological indices of book graph. Journal of Discrete Mathematical Sciences and Cryptography, 23(6) : 1217-1237 (2020). https://doi.org/10.1080/09720529.2020.1809115.
[19] D. Kim, Y.S. Kwon and J. Lee. Enumerations of finite topologies associated with a finite graph. Kyungpook Math. J., 54(4):655-665, 2014. https://doi.org/10.5666/KMJ.2014.54.4.655.
[20] V. Krishnamurthy. On the number of topologies on a finite set. The American Mathematical Monthly, 73(2) : 154-157 (1966). https://doi.org/10.2307/2313548.
[21] C. Marijuan. Finite topologies and digraphs. Proyecciones Journal of Mathematics, 29(3) : 291-307 (2010). https://doi.org/10.4067/S0716-0917201000 0300008.
[22] K. Ragnarsson and B.E. Tenner. Obtainable sizes of topologies on finite sets. J. Comb. Theory, Ser. A, 117(2) : 138-151 (2010). DOI:10.1016/j.jcta.2009.05.002.
[23] V.I. Rodionov. A relation in finite topologies. Journal of Soviet Mathematics, 24(4) : 458-460 (1984). https://doi.org/10.1007/BF01094380.
[24] V.I. Rodionov. Some recurrence relations in finite topologies. Journal of Soviet Mathematics, 27(4) : 2963-2968 (1984). https://doi.org/10.1007/BF01410750.
[25] V.I. Rodionov. On the number of labeled acyclic digraphs. Discrete Mathematics, 105(1-3) : 319-321 (1992). https://doi.org/10.1016/0012-365X(92) 90155-9.
[26] V.I. Rodionov. On enumeration of posets defined on finite set. Siberian Electronic Mathematical Reports, 13 : 318-330 (2016). https://doi.org/10.17377/ semi.2016.13.026.
[27] V.I. Rodionov. On recurrence relation in the problem of enumeration of finite posets. Siberian Electronic Mathematical Reports, 14 : 98-111 (2017). https://doi.org/10.17377/semi.2017.14.011.
[28] V.I. Rodionov. On recursion relations in the problem of enumeration of posets. Siberian Electronic Mathematical Reports, 17 : 190-207 (2020). https://doi.org/10.33048/semi.2020.17.014.
[29] I.G. Velichko, P.G. Stegantseva and N.P. Bashova. The listing of topologies close to the discrete one on finite sets. Russian Mathematics, 59(11) : 19-25 (2015). https://doi.org/10.3103/S1066369X1511002X.




