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Ijraset Journal For Research in Applied Science and Engineering Technology

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Lehmer-4 Mean Labeling of Graphs

Authors: Dr P Shalini, S. A. Meena

DOI Link: https://doi.org/10.22214/ijraset.2022.48176

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Abstract

A graph G=(V,E) with p vertices and q edges is called Lehmer-4 mean graph, if it is possible to label verticesx?V with distinct label g(x) from 2,4,6,8,.….…... 2p in such a way thatwhen eachedge e=uv islabeledwithg(e=uv)= (or) ,then the edge labels are distinct. In this case,g is called Lehmer-4 meanlabelingof G. Inthis paper, Lehmer-4 mean labeling have been introduced.

Introduction

Conclusion

Finally, we conclude that path, comb, Pn?K1,2, Pn?K1,3is a Lehmer-4 mean graph.

References

[1] Bodendick, R. and Walther, G., On number theoretical methods in graph labelingsRes.Exp. Maths (2,/1995) 3-25. [2] Bloom, D.F. Hsu, On graceful directed graphs, SIAMJ, Alg. Discrete Math.,6(1985),519-536. [3] Gallian, M.A., “A Dynamic survey of graph labelings” Electronic journal, 2000 (Volume-23). [4] Harary, F., Graph Theory, New Delhi: Narosa Publishing House, 2001. [5] Hedge, S.M., Labeled graphs and Digraphs: Theory and Application. [6] MacDougall, J.A., Mikra Millar, Slamin and W.D Wallis, Utilitas Math in press. [7] Murugan, K., Subramanian, A., Skolem Difference Mean Graphs, Mapana, Christ University Journal of Science. [8] Palanikumar, R, Rameshkumar, A, Wiener Index of Physio-Chemical Labeled Graph, Bulletin of pure and Applied Sciences, Vol. 37E(Math & Stat), No. 2, 2018, PP: 519 – 522. [9] Palanikumar, R, Rameshkumar, A, T Wiener Index of Fibonacci Labeled Graph Pn F4, Journal of Computer and Mathematical Sciences, Vol. 9(11), 1712 - 1716,November 2018.. [10] Palanikumar, R, Rameshkumar, A, Labeling on Dragon curve Fractal Graph, Aryabhatta Journal of Mathematics & Informatics, Vol. 10, No. 2, July - Dec 2018. [11] Rameshkumar, A, Palanikumar, R, The Wiener Lower Sum and Upper Sum of Friendship Graph , Journal of Indian Acad. Math, Vol. 37, No. 2(2015), pp. 305 – 311. [12] Rameshkumar, A, Palanikumar, R, Wiener Lower Sum of Complete Graph, Aryabhatta Journal of Mathematics & Informatics, Vol. 7, No. 2, July – Dec 2015. [13] Shalini. P, Paul Dhayabaran. D, An Absolute Differences of Cubic and Square Difference Labeling, International Journal of Advanced Scientific and Technical Research, May-June 2015, Issue-5, Volume-3, pages1-8. [14] Shalini. P, Paul Dhayabaran. D, A Study on Root Mean Square Labelings in Graphs, International Journal of Engineering Science and Innovative Technology, May 2015, Volume-4, Issue-3, pages305-309. [15] Shalini. P, Gowri. R, Paul Dhayabaran. D,An absolute Differences of Cubic and Square Difference Labeling For Some Families of Graphs, International Journal of Analytical and Experimental Modal Analysis, Vol.11, Issue 10, October 2019, Pages 538 - 544, Impact Factor: 6.3. ISSN No: 0886 - 9367. [16] Shalini. P, Gowri. R, Paul Dhayabaran. D, An Absolute Differences of Cubic and Square Difference Labeling for Some Shadow and Planar Graphs, The International Journal of Analytical and Experimental Modal Analysis, Volume XII, Issue I, January 2020, Pages 352 – 355.. [17] Shalini. P, Paul Dhayabaran. D, Maximization of Multiplicative Labeling, International Journal of Research in Advent Technology, Special Issue, pages 209-214, January 2019. [18] Shalini. P, Paul Dhayabaran. D,Minimization of Multiplicative Graphs, International Journal of Current Research, Volume 7, Issue-08,pages 19511-19518,August 2015. [19] Shalini. P, Sri Harini. S ,PaulDhayabaran. D,Sum of an Absolute Differences of Cubic And Square Difference Labeling For Cycle Related Graphs, The International Journal of Analytical and Experimental Model Analysis, Volume XII, Issue I, January 2020 , pages 370-374. [20] Shalini. P, Subha. P, Paul Dhayabaran. D,A Study on Disconnected Graphs for an Absolute Difference Labeling, The International Journal of Analytical and Experimental Modal Analysis, Volume XII, Issue I, January 2020, Pages 415 – 421. [21] Shalini. P, Sri Harini. S, Paul Dhayabaran. D,Sum of an Absolute Differences of Cubic And Square Difference Labeling For Path Related Graphs, Infokara Research, Volume IX, Issue 2, February 2020, pages 58 - 67 , ISSN NO: 1021 - 9056. [22] Shalini. P, Subha. P, Paul Dhayabaran. D,A Study On Disconnected Graphs For Sum of an Absolute Difference of Cubic and Square Difference Labeling, Journal Of Interdisciplinary Cycle Research, Volume XII, Issue II, February 2020, Pages 952 - 962, ISSN NO: 0022 - 1945. [23] Shalini. P, Sudar. A, Minimization of Multiplicative labelling for some families of Graphs, Gorteria Journal, Vol 34, Issue 1, 2021, Pg.No: 369 – 376, ISSN No: 0017 - 2294. [24] Shalini. P, Sudar. A,Minimization of Multiplicative labelling for Antenna, Dumpy Level Instrument, Net Graphs, International Journal of analytical and experimental modal analysis, Vol XIII, Issue II, February 2021, Pg.No: 343 – 349, ISSN No: 0886 - 9367.

Copyright

Copyright © 2022 Dr P Shalini, S. A. Meena. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ijraset48176

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Paper Id : IJRASET48176

Publish Date : 2022-12-16

ISSN : 2321-9653

Publisher Name : IJRASET

DOI Link : Click Here