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Journal of Applied Mathematics and Computing

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26-08-2021 | Original Research

Randic index of bipolar fuzzy graphs and its application in network systems

Authors: Soumitra Poulik, Sankar Das, Ganesh Ghorai

Published in: Journal of Applied Mathematics and Computing | Issue 4/2022

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Abstract

Connectivity can be used to measure the strength and combined power of a connected network system. Randic index of graph is one such parameter and it can measure the total combined power of a connected graphical transmission system. For two opposite sided opinion of vertices as well as edges in a bipolar fuzzy graph, it can measure the uncertainty of vertices and edges along positive and negative sides. In this article, the Randic index of bipolar fuzzy graph and bipolar fuzzy subgraph are introduced with their properties. The upper and lower boundaries of Randic index of bipolar fuzzy graphs are studied with some isomorphic properties. Randic index of directed bipolar fuzzy graphs are introduced. Several formula’s are presented to calculate the Randic index of different types of regular bipolar fuzzy graphs and bipolar fuzzy cycles. Finally, two real life applications of Randic index in bipolar fuzzy graphs are described.

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Akram, M.: Bipolar fuzzy graphs. Inf. Sci. 181(24), 5548–5564 (2011)MathSciNetCrossRef

Akram, M.: Bipolar fuzzy graphs with applications. Knowl. Based Syst. 39, 1–8 (2013)CrossRef

Akram, M.: \(m\)-Polar Fuzzy Graphs: Theory. Methods & Applications. Springer, Berlin (2018)MATH

Akram, M., Akmal, R., Alshehri, N.: On \(m\)-polar fuzzy graph structures. SpringerPlus 5, 1448 (2016)CrossRef

Akram, M., Ali, G., Butt, M.A., Alcantud, J.C.R.: Novel MCGDM analysis under \(m\)-polar fuzzy soft expert sets. Neural Comput. Appl. (2021). https://doi.org/10.1007/s00521-021-05850-wCrossRef

Akram, M., Amzad, U., Davvaz, B.: Decision-making analysis based on bipolar fuzzy \(N\)-soft information. Comput. Appl. Math. 40, 180 (2021)MathSciNetCrossRef

Akram, M., Farooq, A.: Bipolar fuzzy tree. New Trends Math. Sci. 4(3), 58–72 (2016)MathSciNetCrossRef

Akram, M., Karunambigal, M.G.: Metric in bipolar fuzzy graphs. World Appl. Sci. J. 14(12), 1920–1927 (2011)

Akram, M., Sarwar, M., Dudek, W.A.: Graphs for the Analysis of Bipolar Fuzzy Information. Springer, Berlin (2020)MATH

10.

Akram, M., Waseem, N.: Novel applications of bipolar fuzzy graphs to decision making problems. J. Appl. Math. Comput. 56, 73–91 (2018)MathSciNetCrossRef

11.

Binu, M., Mathew, S., Mordeson, J.N.: Wiener index of a fuzzy graph and application to illegal immigration networks. Fuzzy Sets Syst. 384, 132–147 (2020)MathSciNetCrossRef

12.

Cederbaum, I.: Some applications of graph theory to network analysis and synthesis. IEEE Trans. Circuits Syst. 31(1), 64–68 (1984)CrossRef

13.

Das, S., Ghorai, G.: Analysis of the effect of medicines over bacteria based on competition graphs with picture fuzzy environment. Comput. Appl. Math. 39, 183 (2020)MathSciNetCrossRef

14.

Das, S., Ghorai, G., Pal, M.: Certain competition graphs based on picture fuzzy environment with applications. Artif. Intell. Rev. (2020). https://doi.org/10.1007/s10462-020-09923-5CrossRefMATH

15.

Ghorai, G., Pal, M.: A note on “Regular bipolar fuzzy graphs” Neural Comput. Appl 21(1), 197–205 (2012) Neural Comput. Appl. 30(5), 1569–1572 (2018)

16.

Ghorai, G., Pal, M.: Some isomorphic properties of \(m\)-polar fuzzy graphs with applications. SpringerPlus 5(1), 2104 (2016)CrossRef

17.

Ghorai, G.: Characterization of regular bipolar fuzzy graphs. Afrika Matematika 32(5), 1043–1057 (2021)MathSciNetCrossRef

18.

Kaveh, A., Rahami, H., Shojaei, I.: Swift Analysis of Civil Engineering Structures Using Graph Theory Mathods. Springer, Berlin (2020)CrossRef

19.

Masarwah, A.A., Qamar, M.A.: Some new concepts of fuzzy soft graphs. Fuzzy Inf. Eng. 8(4), 427–438 (2016)MathSciNetCrossRef

20.

Masarwah, A.A., Qamar, M.A.: Certain types of fuzzy soft graphs. New Math. Natural Comput. 14(02), 145–156 (2018)MathSciNetCrossRef

21.

Mathew, S., Sunitha, M.S., Anjali, N.: Some connectivity concepts in bipolar fuzzy graphs. Ann. Pure Appl. Math. 7(2), 98–100 (2014)

22.

Mathew, S., Sunitha, M.S.: Types of arcs in a fuzzy graph. Inf. Sci. 179(11), 1760–1768 (2009)MathSciNetCrossRef

23.

Minoli, D.: Combinatorial graph complexity, Atti della Accademia Nazionale dei Lincei. Class di Scienze Fisiche. Matematiche e Naturali. Rendiconti 59(6):651–661 (1975)

24.

Mordeson, J.N., Nair, P.S.: Fuzzy Graphs and Fuzzy Hypergraphs. Physica-Verlag, Berlin (2000)CrossRef

25.

Nawaz, H.S., Akram, M.: Oligopolistic competition among the wireless internet service providers of Malaysia using fuzzy soft graphs. J. Appl. math. Comput. (2021). https://doi.org/10.1007/s12190-021-01514-zMathSciNetCrossRefMATH

26.

Poulik, S., Ghorai, G.: Certain indices of graphs under bipolar fuzzy environment with applications. Soft Comput. 24(7), 5119–5131 (2020)CrossRef

27.

Poulik, S., Ghorai, G.: Determination of journeys order based on graphs Wiener absolute index with bipolar fuzzy information. Inf. Sci. 545, 608–619 (2021)MathSciNetCrossRef

28.

Poulik, S., Ghorai, G.: Detour g-interior nodes and detour g-boundary nodes in bipolar fuzzy graph with applications. Hacettepe J. Math. Stat. 49(1), 106–119 (2020)MathSciNetMATH

29.

Poulik, S., Ghorai, G.: Empirical results on bipolar fuzzy graphs with their degree. Missouri J. Math. Sci. 32(2), 211–226 (2020)MathSciNetCrossRef

30.

Poulik, S., Ghorai, G.: Note on bipolar fuzzy graphs with applications. Knowl. Based Syst. 192, 1–5 (2020)CrossRef

31.

Poulik, S., Ghorai, G., Xin, Q.: Pragmatic results in Taiwan education system based IVFG & IVNG. Soft Comput. (2020). https://doi.org/10.1007/s00500-020-05180-4CrossRef

32.

Randic, M.: Characterization of molecular branching. J. Am. Chem. Soc. 97(23), 6609–6615 (1975)CrossRef

33.

Rosenfield, A.: Fuzzy graphs. Fuzzy Sets and Their Application (L. A. Zadeh, K. S. Fu, M. Shimura, Eds.): Academic press, New York, 77-95, (1975)

34.

Shahzadi, S., Rasool, A., Sarwar, M., Akram, M.: A framework of decision making based on bipolar fuzzy competition hypergraphs. J. Intell. Fuzzy Syst. (2021). https://doi.org/10.3233/JIFS-210216CrossRef

35.

Sarwar, M., Akram, M., Shahzadi, S.: Bipolar fuzzy soft information applied to hypergraphs. Soft Comput. 25(2), 1–23 (2021)

36.

West, D.B.: Introduction to Graph Theory, Pearson Education India (2002)

37.

Yager, R.R., Alajlan, N.: Approximate reasoning with generalized orthopair fuzzy sets. Inf. Fusion 38, 65–73 (2017)CrossRef

38.

Yager, R.R., Alajlan, N., Bazi, Y.: Aspects of generalized orthopair fuzzy sets. Int. J. Intell. Syst. 33(11), 2154–2174 (2018)CrossRef

39.

Yang, H.L., Li, S.G., Yang, W.H., Lu, Y.: Notes on bipolar fuzzy graphs. Inf. Sci. 242, 113–121 (2013)MathSciNetCrossRef

40.

Yang, H.L., Li, S.G., Wang, S., Wang, J.: Bipolar fuzzy rough set model on two different universes and its application. Knowl. Based Syst. 35, 94–101 (2012)CrossRef

41.

Zadeh, L.A.: Fuzzy sets. Inf Control 8(3), 338–353 (1965)CrossRef

42.

Zhang, W.R.: Bipolar fuzzy sets and relations: a computational framework for cognitive modeling multiagent decision analysis. Proceeding of IEEE Conference 305–309 (1994)

43.

Zhang, X., Zhao, Y., Zhou, L., Dong, W., Zhang, M., Lv, X.: Transmission tower tilt monitoring system using low-power wide-area network technology. IEEE Sensors J. (2020). https://doi.org/10.1109/JSEN.2020.3004817CrossRef

Title: Randic index of bipolar fuzzy graphs and its application in network systems
Authors: Soumitra Poulik
Sankar Das
Ganesh Ghorai
Publication date: 26-08-2021
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 4/2022
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-021-01619-5

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