Fuzzy Radio Reciprocal L-Labeling on Certain Chemical Graphs

T Bharathi; S Antony Vinoth; S Leo

doi:10.17485/IJST/v14i27.664

Article

Fuzzy Radio Reciprocal L-Labeling on Certain Chemical Graphs

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v14i27.664

Year: 2021, Volume: 14, Issue: 27, Pages: 2284-2292

Original Article

Fuzzy Radio Reciprocal L-Labeling on Certain Chemical Graphs

T Bharathi¹, S Antony Vinoth^2*, S Leo²

¹Assistant Professor, Department of Mathematics, Loyola College, University of Madras,
Chennai, Tamil Nadu, India
²Research Scholar, Department of Mathematics, Loyola College, University of Madras,
Chennai, Tamil Nadu, India

*Corresponding Author
Email: [email protected]

Received Date:19 April 2021, Accepted Date:15 July 2021, Published Date:09 August 2021

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: The objective of this study is to reduce the interference of the signals between Wi-Fi devices where the fuzzy values of the frequencies are from the closed interval [0,1]. Method: A new methodology is introduced to reduce the interference of the signals between Wi-Fi devices that is fuzzy radio reciprocal L-labeling. Findings: Here the general formula of fuzzy radio reciprocal L-labeling has been newly introduced to apply this concept in chemical graphs. Further results and discussions are also proved in this connection using the fuzzy chemical graph structure, where the distance and the frequencies between the routers of Wi-Fi connections are assigned fuzzy weights based on fuzzy radio reciprocal L-labeling, so that interference can be reduced and the signal strength is optimized.

Keywords: Nano sheet; Sirpinski gasket graph ( S n ); Sirpinski like graph (S (n; 4)); g ( s) weight of lines; t (a) weight of points

References

Hale WK. Frequency assignment: Theory and application. In: Proceeding of the IEEE. (Vol. 68, pp. 1497-1514) 1980.
JR. Griggs Labeling Graphs with a Condition at Distance 2. Siam Journal on Discrete Mathematics. 1992;5(4):586–595.
Heuvel JVD, Leese RA, MAS. Shepherd Graph labeling and radio channel assignment. Journal of Graph Theory. 1998;29(4):263–283. Available from: https://dl.acm.org/doi/10.5555/1379171.1379176
Shao Z, Zhang D. The L(2,1)- labeling on graphs and the frequency assignment problem. Applied Mathematics Letters. 2008;21(1):37–41. Available from: https://doi.org/10.1016/j.aml.2006.08.029
Gani AN, Radha K. The Degree of a Vertex in some Fuzzy Graphs. International Journal of Algorithms, Computing and Mathematics, Eashwar Publications. 2009;3(2):107–116.
Panigrahi AP. Survey on Radio k-Colorings of Graphs. AKCE International Journal of Graphs and Combinatorics. 2009;6(1):161–169. Available from: 10.1080/09728600.2009.12088883
Massa'deh MO, Gharaibeh KN. Some Properties on Fuzzy Graphs. Advances in Fuzzy Mathematics. Research India Publications. 2011;2(6):245–252. Available from: http://www.ripublication.com/afm.htm
Gani AN, RS. A Note on Fuzzy Labeling. International Journal of Fuzzy Mathematical Archive. 2014;4(2):88–95.
Nagoorgani A, Subahashini DR. Fuzzy Labeling Tree. International Journal of Pure and Apllied Mathematics. 2014;90(2):131–141. Available from: https://dx.doi.org/10.12732/ijpam.v90i2.3
Tom M, Sunith MS. Muraleedhtan Shetty sunith. Strong sum distance in fuzzy graph. Springar Plus. 2015;4(214). Available from: https://doi.org/10.1186/s40064-015-0935-5
Nazeer S, Khan S, Kausar I, Nazeer W. Radio Labelling and Radio Number for Generalized Caterpillar Graphs. Journal of Applied Mathematics and Informatics. 2016;34(6):551–565. Available from: 10.14317/jami.2016.451
Mahapatra R, Samanta S, Allahviranloo T, Pal M. Madhumangal Pal. Radio fuzzy graphs and assignment of frequency in radio stations. Computational and Applied Mathematics. 2019;38(4):1–2. Available from: https://link.springer.com/article/10.1007/s40314-019-0888-3
John BS, Mela JV. Radio labeling of complete related graphs. Compliance Engineering Journal. 2020;11(2):173–187.
Uma J, Bhargavi RM. Radio labeling on some corona graphs. AIP Conference Proceeding. 2020;2227:1–7. Available from: https://doi.org/10.1063/5.0025217
Chavez A, Liu DDF, Shurman M. Optimal radio-k-labelings of trees. European Journal of Combinatorics. 2021;91(91):103203. Available from: https://dx.doi.org/10.1016/j.ejc.2020.103203
Chartrand G, Erwin D, Zhang P. A graph labelling problem suggested by FM channel restrictions. Bull. Inst. Combin. Appl. 2005;43(114):43–57.
Mordeson JN, Nair PS. Series Title Studies in Fuzziness and Soft Computing. In: Fuzzy Graphs and Fuzzy Hypergraphs (1). (pp. 19-81) 2000.
Sunitha MS, Mathew S. Fuzzy Graph Theory: A Survey. Annals of Pure and Applied Mathematics. 2013;4(1):92–110.
Gani AN, Akram M, Subahashini DR(. Novel Properties of Fuzzy Labeling Graphs. Journal of Mathematics. 2014;2014(70):1–6. Available from: https://dx.doi.org/10.1155/2014/375135
Xavier A, Theresal SS, Raja MJ. Induced H-packing K-Partition number for certain nanotubes and chemical graphs. Journal of Mathematical Chemistry. 2020;(58) 1177–1196. Available from: https://link.springer.com/article/10.1007/s10910-020-01124-3
Xavier DA, Rosary M, Arokiaraj A. Topological Properties of Sierpinski Gasket Rhombus Graphs. International Journal of Mathematics and Soft Computing. 2014;4(2):95. Available from: https://dx.doi.org/10.26708/ijmsc.2014.2.4.10
Vinoth SA, Bharathi T. Radio Reciprocal Membership Function on Cycle Related Graphs. International Journal of Recent Technology and Engineering. 2019;4(8). Available from: https://www.ijrte.org/wp-content/uploads/papers/v8i4/B3583078219.pdf

Copyright

© 2021 Bharathi et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)