Novel concepts of the Randic index in vague graphs with applications

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

10.22075/ijnaa.2023.30895.4513

Abstract

A topological index is a numerical quantity for the structure graph of the molecule and it can be represented through graph theory. Also, its application not only in the field of chemistry can also be applied in areas including computer science, networking, etc. Hence, this paper introduces the Randic index of a vague graph and vague subgraph with their properties. The upper and lower boundaries of the Randic index of vague graphs are studied with some isomorphic properties. Likewise, the Randic index of directed vague graphs is introduced. Finally, an application of the Randic index in construction has been presented.

Keywords

[1] M. Akram, A. Farooq, A.B. Saeid, and K.P. Shum, Certain types of vague cycles and vague trees, J. Intell. Fuzzy Syst. 28 (2015), no. 2, 621–631
[2] M. Akram, N. Gani, and A.B. Saeid, Vague hypergraphs, J. Intell. Fuzzy Syst. 26 (2014), 647–653.
[3] R.A. Borzooei and H. Rashmanlou, Ring sum in product intuitionistic fuzzy graphs, J. Adv. Res. Pure Math. 7 (2015), no. 1, 16–31.
[4] R.A. Borzooei and H. Rashmanlou, Domination in vague graphs and its applications, J. Intell. Fuzzy Syst. 29 (2015), 1933–1940.
[5] R.A. Borzooei and H. Rashmanlou, Degree of vertices in vague graphs, J. Appl. Math. Inf. 33 (2015), no. 5, 545–557.
[6] R.A. Borzooei, H. Rashmanlou, S. Samanta, and M. Pal, Regularity of vague graphs, J. Intell. Fuzzy Syst. 30 (2016), 3681–3689.
[7] M. Binu, S. Mathew, and J.N. Mordeson, Connectivity index of a fuzzy graph and its application to human trafficking, Fuzzy Sets Syst. 360 (2019), 117–136.
[8] W.L. Gau and D.J. Buehrer, Vague sets, IEEE Trans. Syst. Man Cybernet. 23 (1993), no. 2, 610–614.
[9] A. Kauffman, Introduction a la Theorie des Sous-Ensembles Flous a l’usage des ingenieurs, Vol. 1, Elements Theoriques de Base, Masson, Paris, 1973.
[10] J.N. Mordeson and P. Chang-Shyh, Operations on fuzzy graphs, Inf. Sci. 79 (1994), no. 3-4, 159–170.
[11] S. Poulik and G. Ghorai, Certain indices of graphs under bipolar fuzzy environment with applications, Soft Comput. 24 (2020), 5119–5131.
[12] S. Poulik and G. Ghorai, Determination of journeys order based on graph’s Wiener absolute index with bipolar fuzzy information, Inf. Sci. 545 (2021), 608–619.
[13] S. Poulik and G. Ghorai, Detour g-interior nodes and detour g-boundary nodes in bipolar fuzzy graph with applications, Hacettepe J. Math. Stat. 49 (2020), no. 1, 106–119.
[14] S. Poulik and G. Ghorai, Applications of graphs complete degree with bipolar fuzzy information, Complex Intell. Syst. 8 (2022) 1115–1127.
[15] N. Ramakrishna, Vague graphs, Int. J. Cogn. Comput. 7 (2009), 51–58.
[16] H. Rashmanlou and R.A Borzooei, Vague graphs with application, J. Intell. Fuzzy Syst. 30 (2016), 3291–3299.
[17] H. Rashmanlou, S. Samanta, M. Pal, and R.A Borzooei, A study on bipolar fuzzy graphs, J. Intell. Fuzzy Syst. 28 (2015), 571–580.
[18] H. Rashmanlou and R.A Borzooei, Product vague graphs and its applications, J. Intell. Fuzzy Syst. 30 (2016), 371–382.
[19] H. Rashmanlou, S. Samanta, M. Pal, and R.A Borzooei, Intuitionistic fuzzy graphs with categorical properties, Fuzzy Inf. Engin. 7 (2015), no. 3, 317–334.
[20] H. Rashmanlou, S. Samanta, M. Pal, and R.A Borzooei, Bipolar fuzzy graphs with Categorical properties, Int. J. Comput. Intell. Syst. 8 (2015), no. 5, 808–818.
[21] Y. Rao, S. Kosari, Z. Shao, X. Qiang, M. Akhoundi, and X. Zhang, Equitable domination in vague graphs with application in medical sciences, Front. Phys. 9 (2021), 635642.
[22] Y. Rao, S. Kosari, and Z. Shao, Certain properties of vague graphs with a novel application, Mathematics 8 (2020), no. 10, 1647.
[23] Y. Rao, S. Kosari, Z. Shao, R. Cai, and L. Xinyue, A Study on Domination in vague incidence graph and its application in medical sciences, Symmetry 12 (2020), no. 11, 1885.
[24] A. Rosenfeld, Fuzzy graphs, fuzzy sets and their applications, Zadeh, L.A., Fu, K.S., Shimura, M., Eds.; Academic Press: New York, NY, USA, 1975, pp. 77–95.
[25] S. Samanta and M. Pal, Irregular bipolar fuzzy graphs, Int. J. Appl. Fuzzy Sets 2 (2012), 91–102.
[26] A. Sebastian, J.N Mordeson and S. Mathew, Generalized fuzzy graph connectivity parameters with application to human trafficking, Mathematics 8 (2020), no. 3, 424.
[27] Z. Shao, S. Kosari, H. Rashmanlou, and M. Shoaib, New concepts in intuitionistic fuzzy graph with application in water supplier systems. Mathematics 8 (2020), no. 8, 1241.
[28] A.A Talebi, H. Rashmanlou, and N. Mehdipoor, Isomorphism on vague graphs, Ann. Fuzzy Math. Inf. 6 (2013), no. 3, 575–588.
[29] Y. Talebi and H. Rashmanlou, Application of dominating sets in vague graphs, Appl. Math. E-Notes 17 (2017), 251–267.
[30] L.A Zadeh, Fuzzy sets, Inf. Control 8 (1965), 338–353.
[31] L.A. Zadeh, Similarity relations and fuzzy ordering, Inf. Sci. 3 (1971), 177–200.
[32] L.A. Zadeh, Is there a need for fuzzy logic?, Inf. Sci. 178 (2008), 2751–2779.
[33] S. Zeng, M. Shoaib, H. Ali, F. Smarandache, H. Rashmanlou, and F. Mofidnakhaei, Certain properties of single valued neutrosophic graph with application in food and agriculture organization, Int. J. Comput. Intell. Syst. 14 (2021), no. 1, 1516–1540.

Articles in Press, Corrected Proof
Available Online from 07 January 2024
  • Receive Date: 10 June 2023
  • Revise Date: 28 October 2023
  • Accept Date: 14 November 2023