A New Approach of Perfect Domination in Product of Interval-Valued Fuzzy Incidence Graphs With Application

Authors

  • K. Kalaiarasi PG and Research Department of Mathematics, Cauvery College for Women (Autonomous) (affiliated to Bharathidasan University), Trichy 620018, Tamil Nadu, India; Department of Mathematics, Srinivas University, Surathkal, Mangaluru 574146, Karnataka, India https://orcid.org/0000-0001-6705-5354
  • P. Geethanjali PG and Research Department of Mathematics, Cauvery College for Women (Autonomous) (affiliated to Bharathidasan University), Trichy 620018, Tamil Nadu, India https://orcid.org/0000-0002-7903-2165

DOI:

https://doi.org/10.26713/cma.v13i2.1720

Keywords:

. Interval-valued Fuzzy Incidence Graph, Cartesian product of two IVFIGs, Tensor product of two IVFIGs, Perfect dominating set

Abstract

Fuzzy graphs, also known as fuzzy incidence graphs, are a useful and well-organized tool for encapsulating and resolving a variety of real-world situations involving ambiguous data and information. In this investigation article, we introduced the chance of interval-valued fuzzy incidence graphs (IVFIGs) alongside their specific properties. The operations of Cartesian product (CP), Tensor product (TP) in IVFIGs are additionally examined. The technique to compute the degree (DG) of IVFIGs acquired by CP and TP is examined. Some significant hypotheses to figure the DG of the vertices of IVFIGs gained by CP and TP are explained. An innovative idea of perfect domination in CP of two IVFIGs and TP of two IVFIGs utilizing incidence pair are presented and gotten the connection between them. Eventually, genuine utilization of perfect domination number (PDN) to discover which countries (country) have the best education policies among various countries is inspected.

Downloads

Download data is not yet available.

References

K.T. Atanassov, Intuitionistic Fuzzy Sets, Theory and Applications, Springer, New York, USA (1999), DOI: 10.1007/978-3-7908-1870-3.

C. Berge, Theory of Graphs and its Applications, Methuen, London (1962).

T.J. Bhatt and G.C. Bhimani, Perfect domination number of path graph Pn and its corona product with another path graph Pn−1, Malaya Journal of Matematik 9(1) (2021), 118 – 123, DOI: 10.26637/MJM0901/0020.

A. Bozhenyuk, S. Belyakov, M. Knyazeva and I. Rozenberg, On computing domination set intuitionistic fuzzy graph, International Journal of Computational Intelligence Systems 14(1) (2021), 617 – 624, DOI: 10.2991/ijcis.d.210114.002.

P. Debnath, Domination in interval valued fuzzy graphs, Annal of Fuzzy Mathematics and Informatics 6(2) (2013), 363 – 370, URL: http://www.afmi.or.kr/papers/2013/Vol-06_No-02/AFMI-6-2(227--453)/AFMI-6-2(363--370)-J-121204R1.pdf.

K. Dharmalingan and P. Nithya, Excellent domination in fuzzy graphs, Bulletin of the International Mathematical Virtual Institute 7 (2017), 257 – 266.

T. Dinesh, Fuzzy incidence graph – an introduction, Advances in Fuzzy Sets and Systems 21(1) (2016), 33 – 48, DOI: 10.17654/FS021010033.

A.N. Gani and S.S. Begum, Degree, order and size in intuitionistic fuzzy graphs, International Journal of Algorithms, Computing and Mathematics 3(3) (2010), 11 – 16.

M.B. Gorzalczany, A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and System 21 (1987), 1 – 17, DOI: 10.1016/0165-0114(87)90148-5.

M.B. Gorzalczany, An interval-valued fuzzy inference method some basic properties, Fuzzy Sets and System 31 (1989), 243 – 251, DOI: 10.1016/0165-0114(89)90006-7.

T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York (1998), DOI: 10.1201/9781482246582.

A.M. Ismayil and H.S. Begum, Accurate split (non split) domination in fuzzy graphs, Advances and Applications in Mathematical Sciences 20(5) (2021), 839 – 851.

K. Kalaiarasi and L. Mahalakshmi, An Introduction to Fuzzy strong graphs, Fuzzy soft graphs, complement of fuzzy strong and soft graphs, Global Journal of Pure and Applied Mathematics 13(6) (2017), 2235 – 2254.

O.T. Manjusha and M.S. Sunitha, Covering, matchings and paired domination in fuzzy graphs using strong arcs, Iranian Journal of Fuzzy Systems 16(1) (2019), 145 – 157, DOI: https://ijfs.usb.ac.ir/article_4490_228b479d226982483d1ff454ca823d10.pdf.

O.T. Manjusha and M.S. Sunitha, Strong domination in fuzzy graphs, Fuzzy Information and Engineering 7(3) (2015), 369 – 377, DOI: 10.1016/j.fiae.2015.09.007.

S. Mathew and J.N. Mordeson, Connectivity concepts in fuzzy incidence graphs, Information Sciences 382-383 (2017), 326 – 333, DOI: 10.1016/j.ins.2016.12.020.

J.N. Mordeson and P. Chang-Shyh, Operations on fuzzy graphs, Information Sciences 79(3-4) (1994), 159 – 170, DOI: 10.1016/0020-0255(94)90116-3.

A. Nagoorgani and V.T. Chandrasekaran, Domination in fuzzy graph, Advances in Fuzzy Sets and Systems I(1) (2016), 17 – 26.

I. Nazeer, T. Rashid and A. Keikha, An application of product of intuitionistic fuzzy graphs in textile industry, Complexity 2021 (2021), 16 pages, DOI: 10.1155/2021/5541125.

I. Nazeer, T. Rashid, M. Tanveer and J.L.G. Guirao, Domination in join of fuzzy incidence graphs using strong pairs with Application in trading system of different countries, Symmetry 2021 (2021), 13, 1279, 15 pages, DOI: 10.3390/sym13071279.

M. Pal, S. Samanta and H. Rashmanlou, Some results on interval-valued fuzzy graphs, International Journal of Computer Science and Electronic Engineering 3(3) (2015), 205 – 211.

R. Parvathi and M. Karunambigai, Intuitionistic Fuzzy Graphs, Computational Intelligence, Theory and Applications, Springer, New York, USA (2006), DOI: 10.1007/3-540-34783-6_15.

R. Parvathi, M.G. Karunambigai and K.T. Atanassov, Operations on intuitionistic fuzzy graphs, in: Proceedings of the FUZZ-IEEE 2009, IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, August 2009, DOI: doi.org/10.1109/FUZZY.2009.5277067.

N. Patra, T. Pramanik, M. Pal and S. Mondal, Cliques and clique covers in inter-valued fuzzy graphs, International Journal of Computational Intelligence Systems 14(1) (2021), 1773 – 1783, DOI: 10.2991/ijcis.d.210610.001.

O. Ore, Theory of Graphs, American Mathematical Society Colloquium Publications, 38 (American Mathematical Society, Providence, RI) (1962).

H. Rashmanlou and M. Pal, Some properties of highly irregular interval-valued fuzzy graphs, World Applied Sciences Journal 27(12) (2013), 1756 – 1773, URL: https://www.idosi.org/wasj/wasj27(12)13/32.pdf.

S. Revathi and C.V.R. Harinarayaman, Equitable domination in fuzzy graphs, International Journal of Engineering Research and Applications 4(6) (2014), 80 – 83.

M.K. Roy and R. Biswas, I-V fuzzy relations and Sancher’s approach for medical diagnosis, Fuzzy Sets and System 47 (1992), 35 – 38, DOI: 10.1016/0165-0114(92)90057-B.

S. Sahoo and M. Pal, Different types of products on intuitionistic fuzzy graphs, Pacific Science Review A: Natural Science and Engineering 17(3) (2015), 87 – 96, DOI: 10.1016/j.psra.2015.12.007.

S. Sahoo and M. Pal, Intuitionistic fuzzy competition graphs, Journal of Applied Mathematics and Computing 52(1-2) (2016), 37 – 57, DOI: 10.1007/s12190-015-0928-0.

S. Sahoo and M. Pal, Intuitionistic fuzzy tolerance graphs with application, Journal of Applied Mathematics and Computing 55(1-2) (2017), 495 – 511, DOI: 10.1007/s12190-016-1047-2.

S. Sahoo and M. Pal, Product of intuitionistic fuzzy graphs and degree, Journal of Intelligent & Fuzzy Systems 32(1) (2017), 1059 – 1067, DOI: 10.3233/JIFS-16348.

S. Sahoo, S. Kosari, H. Rashmanlou and M. Shoib, New concepts in intuitionistic fuzzy graph with application in water supplier systems, Mathematics 8(8) (2020), 1241, DOI: 10.3390/math8081241.

S. Samanta and M. Pal, Fuzzy threshold graphs, CITT International Journal of Fuzzy Systems 3(12) (2011), 360 – 364.

S. Samanta and M. Pal, Fuzzy tolerance graphs, International Journal of Latest Trends in Mathematics 1(2) (2011), 57 – 67.

N. Sarala and T. Kavitha, (1,2)-vertex domination in fuzzy graph, International Journal of Innovative Research in Science, Engineering and Technology 5(9) (2016), 16501 – 16505.

A. Selvam and C.Y. Ponnappan, Domination in join of fuzzy graphs using strong ARCS, Materials Today Proceedings 37 (2021), 67 – 70, DOI: 10.1016/j.matpr.2020.03.257.

A.N. Shain and M.M.Q. Shubatah, Inverse dominating set of an interval-valued fuzzy graphs, Asian Journal of Probability and Statistics 11(3) (2021), 42 – 50, DOI: 10.9734/ajpas/2021/v11i330270.

A. Somasundaram and S. Somasundaram, Domination in fuzzy graphs – I, Pattern Recognition Letters 19(9) (1998), 787 – 791, DOI: 10.1016/S0167-8655(98)00064-6.

D.A. Xavior, F. Isido and V.M. Chitra, On domination in fuzzy graphs, International Journal of Computing Algorithm 2 (2013), 248 – 250.

L.A. Zadeh, Fuzzy sets, Information and Control 8(3) (1965), 338 – 353, DOI: 10.1016/S0019-9958(65)90241-X.

Downloads

Published

17-08-2022
CITATION

How to Cite

Kalaiarasi, K., & Geethanjali, P. (2022). A New Approach of Perfect Domination in Product of Interval-Valued Fuzzy Incidence Graphs With Application. Communications in Mathematics and Applications, 13(2), 625–646. https://doi.org/10.26713/cma.v13i2.1720

Issue

Vol. 13 No. 2 (2022)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.