Proper Colorings in R-Regular Randic Index Graphs

Abstract

The new idea of proper colourings in the r-regular Randic index graph has been proposed in this paper. New Chromatic number inequalities connected to the Randic index are established in this paper.

Introduction

Conclusion

In this paper, new inequality has been established. Further, it has been verified for Randic Index. Finally, we conclude that new inequalities in chromatic numbers are related to RandicIndex.

References

[1] AmalorpavaJerline J., Litta E., Dhanalakshmi K., Benedict Michael Raj L.,F-Index of Generalized Mycielskian Graphs, International Journal of Recent Scientific Research, Volume 10, Issue 6, June 2019,P.No.:32366-32371. [2] Bodendick, R. and Walther, G., On number theoretical methods in graph labelingsRes.Exp.Maths (2,/1995) 3-25. [3] Bloom, D.F. Hsu, On graceful directed graphs, SIAMJ, Alg. Discrete Math.,6(1985),519-536. [4] Felix J., Litta E., Benedict Micheal Raj L., Changing and Unchanging properties of Single Chromatic Transversal Domination Number of Graphs, International Journal of Mathematics Trends and Technology, Volume 52, Issue 4, Dec 2017,P.No.:262-266. [5] Felix J., Litta E., Benedict Micheal Raj L., Single Chromatic Transversal Dominating Irredundant Number for odd cycles, Peterson graph and Mycielski graph, Infokara Research, Volume 8, Issue 10, Oct 2019,P.No.:139-145. [6] Felix J., Litta E., Benedict Micheal Raj L., Single Chromatic Transversal Dominating Irredundant Number of graphs, Adalya Journal, Volume 10, Issue 8, Oct 2019,P.No.:264-272. [7] Harary, F., Graph Theory, New Delhi: Narosa Publishing House, 2001. [8] Litta E., AmalorpavaJerline J.,DhanalakshmiK.,BenedictMicheal Raj L.,andModified Zagreb Indices of Bridge Graphs, International Journal of Mathematical Archive, Volume 8, Issue 3, Mar 2017,P.No.: 86-91. [9] Litta E., AmalorpavaJerline J., Rasika R., F- Co-index of Generalized Mycielskian Graphs, International Journal of Research in Advent Technology, Volume 7, Issue 4, Apr 2019,P.No.:243-249. [10] Litta E., AmalorpavaJerline J., Felix J., Benedict Micheal Raj L.,First and Second Modified Zagreb Indices of Product Graphs, InfokaraResearch,Volume 9, Issue 1, Jan 2020,P.No.: 279-293. [11] Litta, E., Datchini, S, Proper Colourings in r – Regular Zagreb Index Graph”, Aryabhatta Journal of Mathematics and Informatics, Volume 15, Issue 1, Jan -June 2023. Pg. No. 149-154, Impact Factor: 5.856, ISSN No: 0975-7139(P) 2394-9309. [12] Prakash, V., Gopi, R., Shalini, P., Anti Skolem Mean Labeling of Quadrilateral Snake Related Graphs, TuijinJishu/Journal of Propulsion Technology, Vol. 44, No. 5(2023), 495 – 500. [13] Saridha, S. and HaridhaBanu. S, A New Direction Towards Plus weighted Grammar, International Journal for Research in Applied Science and Engineering Technology (IJRASET), ISSN: 2321 – 9653, Vol. 11, Issue II, February 2023. [14] Saridha, S. and Jothika, T, An Introduction to Plus Weighted Dendrolanguage and its properties, Aryabhatta Journal of Mathematics and Informatics, Volume 15, Issue 1, Jan -June 2023. Pg. No. 93-100, Impact Factor: 5.856, ISSN No: 0975-7139(P) 2394-9309. [15] Saridha, S. and HaridhaBanu. S, An Innovative ideas on plus weighted linear grammer, Aryabhatta Journal of Mathematics and Informatics, Volume 15, Issue 2, December 2023. Pg. No. 173 – 178. [16] Shalini. P, Paul Dhayabaran. D., Proper Colourings in Magic and Anti-magic Graph, International Journal of Engineering and Research Technology, Vol. 3, Issue. 2, pages 815-818. February 2014. [17] 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, pages 1-8. [18] 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, pages 305-309. [19] Shalini, P., Gowri, R., Paul Dhayabaran, D., An Absolute Differences of Cubic and Square Difference Labeling For Some Families Of Graphs, The International journal of analytical and experimental modal analysis, Volume XI, Issue 10, October 2019, Page no: 538-544. [20] Shalini, P., Meena, S.A., Lehmer-4 Mean Labeling for Some Path Related Graphs, Aryabhatta Journal of Mathematics and Informatics, Volume 15, Issue 1, Jan -June 2023. Pg. No. 105-110. [21] Shalini, P., Skolem Odd Vertex Graceful Signed Graphs for Star Graphs, International Journal of Mathematics Trends and Technology, Volume 69, Issue 8, August 2023, Pg. No. 30 – 35. [22] Shalini, P., Paul Dhayabaran, D., Maximization of Multiplicative Labeling, International journal of Research in Advent Technology(IJRAT), Special Issue January 2019, Page no: 209-214. [23] Shalini, P., Priyadarshini, K., SP Mean Difference Labeling for Some Families of Graphs”, Research and Applications Towards Mathematics and Computer Science, Volume 9, February 2024, Pg. No. 1-12, B P International, Print ISBN: 978-81-970187-8-7, eBook ISBN: 978-81-970187-9-4.

Copyright

Copyright © 2024 Dr. E. Litta, N. Jayavarshini. 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.