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The strong total Roman domination in fuzzy graphs | ||
| Communications in Combinatorics and Optimization | ||
| دوره 11، شماره 4، اسفند 2026، صفحه 1333-1357 اصل مقاله (615.58 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.31398.2841 | ||
| نویسندگان | ||
| Martin Cera1؛ Pedro Garcia-Vazquez1؛ Juan Carlos Valenzuela Tripodoro* 2 | ||
| 1Departamento de Matemática Aplicada I, Universidad de Sevilla, Spain | ||
| 2Departamento de Matemáticas, Universidad de Cádiz, Algeciras Campus, Spain | ||
| چکیده | ||
| In recent years, domination theory and its variants, including Roman domination, have been widely studied in fuzzy graphs due to their ability to model uncertainty in complex networks such as social, transportation, and biological systems. A strong total Roman dominating function (STRDF) on a fuzzy graph $G=(V,\sigma,\mu)$ is a mapping $f:V\rightarrow \{0,1,2\}$ such that every vertex $u$ with $f(u)=0$ has a strong neighbor labeled 2, and every vertex labeled 1 or 2 has at least one strong neighbor with a non-zero label. The strong total Roman domination number, $\gamma_{sR}^t(G)$, is defined as the minimum weight $\sum_{u\in V} f(u)\mu_s(u)$ among all STRDFs $f,$ where $\mu_s(u)$ denotes the minimum membership value of the strong edges incident to $u$. In this paper, we introduce and study the strong total Roman domination number for fuzzy graphs. We establish several bounds, investigate its realizability, determine exact values for several standard families of fuzzy graphs, and present some applications. | ||
| کلیدواژهها | ||
| Domination؛ total Roman domination؛ fuzzy graphs | ||
| مراجع | ||
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[1] H.A. Ahangar, M.A. Henning, V. Samodivkin, and I.G. Yero, Total Roman domination in graphs, Appl. Anal. Discr. Math. 10 (2016), no. 2, 501–517. https://doi.org/10.2298/AADM160802017A
[2] J. Amjadi., Total Roman domination subdivision number in graphs, Commun. Comb. Optim. 5 (2020), no. 2, 157–168. https://doi.org/10.22049/CCO.2020.26470.1117 [3] J. Amjadi, S. Nazari-Moghaddam, and S.M. Sheikholeslami, Global total Roman domination in graphs, Discret. Math. Algorithms Appl. 9 (2017), no. 4, 1750050. https://doi.org/10.1142/S1793830917500501
[4] J. Amjadi, B. Samadi, and L. Volkmann, Total restrained Roman domination, Commun. Comb. Optim. 8 (2023), no. 3, 575–587. https://doi.org/10.22049/cco.2022.27628.1303
[5] R.A. Borzooei and H. Rashmanlou, Domination in vague graphs and its applications, J. Intell. Fuzzy Syst. 29 (2015), no. 5, 1933–1940. https://doi.org/10.3233/IFS-151671
[6] R.A. Borzooei and H. Rashmanlou, Semi global domination sets in vague graphs with application, J. Intell. Fuzzy Syst. 30 (2016), no. 6, 3645–3652. https://doi.org/10.3233/IFS-162110
[7] Y. Chu, J. Cao, W. Ding, J.S. Huang, H. Ju, H. Cao, and G. Liu, Hyperspectral image classification using feature fusion fuzzy graph broad network, Inf. Sci. 689 (2025), 121504. https://doi.org/10.1016/j.ins.2024.121504
[8] E.J. Cockayne, R.M. Dawes, and S.T. Hedetniemi, Total domination in graphs, Networks 10 (1980), no. 3, 211–219. https://doi.org/10.1002/net.3230100304 [9] E.J. Cockayne, P.A. Dreyer, S.M. Hedetniemi, and S.T. Hedetniemi, Roman domination in graphs, Discrete Math. 278 (2004), 11–22. https://doi.org/10.1016/j.disc.2003.06.004
[10] S.C. García, A.C. Martínez, and I.G. Yero, Quasi-total Roman domination in graphs, Results Math. 74 (2019), no. 4, Article No. 173. https://doi.org/10.1007/s00025-019-1097-5
[11] S.M.M. Golsefid, M.H.F. Zarandi, and S. Bastani, Fuzzy community detection model in social networks, Int. J. Intell. Systems 30 (2015), no. 12, 1227–1244. https://doi.org/10.1002/int.21743
12] J.L. Gross, J. Yellen, and P. Zhang, Handbook of Graph Theory, second edition ed., CRC Press, 2013.
[13] I. Gutiérrez, D. Gómez, J. Castro, and R. Espínola, From fuzzy information to community detection: An approach to social networks analysis with soft information, Mathematics 10 (2022), no. 22, 4348. https://doi.org/10.3390/math10224348
[14] G. Hao, L. Volkmann, and D.A. Mojdeh, Total double Roman domination in graphs, Commun. Comb. Optim. 5 (2020), no. 1, 27–39. https://doi.org/10.22049/CCO.2019.26484.1118
[15] T.W. Haynes, S.T. Hedetniemi, and M.A. Henning, Domination in Graphs: Core Concepts, Springer Monographs in Mathematics, Springer, 2023.
[16] W.A. Khan, W. Arif, H. Rashmanlou, and S. Kosari, Interval-valued picture fuzzy hypergraphs with application towards decision making, J. Appl. Math. Comput. 70 (2024), no. 2, 1103—1125. https://doi.org/10.1007/s12190-024-01996-7
[17] S. Kosari, Z. Shao, Y. Rao, X. Liu, R. Cai, and H. Rashmanlou, Some types of domination in vague graphs with application in medicine, J. Mult.-Valued Log. Soft Comput. 40 (2023), no. 3-4, 203—219.
[18] M.M. Luqman, J.Y. Ramel, J. Lladós, and T. Brouard, Fuzzy multilevel graph embedding, Pattern Recognition 46 (2013), no. 2, 551–565. https://doi.org/10.1016/j.patcog.2012.07.029
[19] O.T. Manjusha and M.S. Sunitha, Strong domination in fuzzy graphs, Fuzzy Inf. Eng. 7 (2015), 369–377. https://doi.org/10.1016/j.fiae.2015.09.007 [20] O.T. Manjusha and M.S. Sunitha, Total domination in fuzzy graphs using strong arcs, Ann. Pure Appl. Math. 9 (2015), no. 1, 23–33.
[21] M. Mojahedfar, A.A. Talebi, and H. Rashmanlo, The novel concept of Roman domination in fuzzy graph, J. Phys. Sciences 28 (2023), 1–9. http://doi.org/10.62424/jps.2023.28.00.01
[22] J.N. Mordeson and J.N.P.S. Nair, Fuzzy graphs and fuzzy hypergraphs, Physica-Verlag, 2000.
[23] A. Nagoor Gani and V.T. Chandrasekaran, Domination in fuzzy graph, Adv. in Fuzzy Sets and Systems 1 (2006), no. 1, 17–26.
[24] A. Nagoor Gani and P. Vijayalakshmi, Insensitive edge in domination of fuzzy graph, Int. J. Contemp. Math. Sciences 6 (2011), no. 26, 1303–1309.
[25] S. Noorjahan and S.S. Basha, The Laplacian energy of an intuitionistic fuzzy rough graph and its utilisation in decision-making, Oper. Res. Decis. 35 (2025), no. 1, 81–107. https://doi.org/10.37190/ord250104
[26] S. Okada, Fuzzy shortest path problems incorporating interactivity among paths, Fuzzy Sets Syst. 142 (2004), no. 3, 335–357. https://doi.org/10.1016/S0165-0114(03)00225-2
[27] Y. Rao, S. Kosari, J. Anitha, I. Rajasingh, and H. Rashmanlou, Forcing parameters in fully connected cubic networks, Mathematics 10 (2022), no. 8, 1263. https://doi.org/10.3390/math10081263
[28] H. Rashmanlou, M. Pal, R.A. Borzooei, F. Mofidnakhaei, and B. Sarkar, Product of interval-valued fuzzy graphs and degree, J. Intell. Fuzzy Syst. 35 (2018), no. 6, 6443–6451. https://doi.org/10.3233/JIFS–181488
[29] S. Rout, P.K. Mishra, and G.K. Das, Total roman domination and total domination in unit disk graphs, Commun. Comb. Optim. 10 (2025), no. 4, 803–823. https://doi.org/10.22049/cco.2024.28647.1650
[30] S. Sahoo, M. Pal, H. Rashmanlou, and R.A. Borzooei, Covering and paired domination in intuitionistic fuzzy graphs, J. Intell. Fuzzy Syst. 33 (2017), no. 6, 4007–4015. https://doi.org/10.3233/JIFS-17848
[31] A. Somasundaram and S. Somasundaram, Domination in fuzzy graphs- I, Pattern Recognit. Lett. 19 (1998), 787–791. https://doi.org/10.1016/S0167-8655(98)00064-6 [32] A.A. Sori, A. Ebrahimnejad, and H. Motameni, The fuzzy inference approach to solve multi-objective constrained shortest path problem, J. Intell. Fuzzy Syst. 38 (2020), no. 4, 4711–4720. https://doi.org/10.3233/JIFS-191413
[33] Y. Talebi and H. Rashmanlou, New concepts of domination sets in vague graphs with applications, Int. J. Comput. Sci. Math. 10 (2019), no. 4, 375—389. https://doi.org/10.1504/ijcsm.2019.102686
[34] L. Volkmann, Signed total Roman domination in graphs, J. Comb. Optim. 32 (2016), no. 3, 855–871. https://doi.org/10.1007/s10878-015-9906-6
[35] L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
[36] Y. Zhang, Z.L. Zhang, Y. Deng, and S. Mahadevan, A biologically inspired solution for fuzzy shortest path problems, Appl. Soft Comput. 13 (2013), no. 5, 2356–2363. https://doi.org/10.1016/j.asoc.2012.12.035
[37] H.J. Zimmermann, Fuzzy set theory–and its applications, Kluwer Academic Publishers, Boston, Dordrecht/London, 2001. | ||
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