• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology

Article

Indian Journal of Science and Technology

Year: 2024, Volume: 17, Issue: 20, Pages: 2038-2042

Original Article

Split Regular Domination in Litact Graphs

Received Date:12 March 2024, Accepted Date:01 April 2024, Published Date:14 May 2024

Abstract

Objectives: In the context of graph theory, a litact graph is a specific type of graph. This study introduces a new domination parameter, called split regular domination in litact graphs. Methods: When we talk about split regular domination in a litact graph during this investigation, we think about how to divide the litact graph into partitions that adhere to specific domination principles by taking a minimal split regular dominating set with all vertices of equal degree. We used a few common definitions and the ideas of several domination parameters in G to obtain the results. Findings: Numerous bounds on were found in relation to the different parameters of G like vertices, edges, diameter, vertex covering number, maximum degree and so forth, and its relationship to other dominating parameters of G such as total domination, edge domination, connected domination and so on was also found. Furthermore, outcomes resembling those of Nordhaus-Gaddum were also obtained. Novelty: Graph G was used to find a litact graph. Subsequently, a few findings of a new domination parameter called split regular domination in a litact graph in terms of different parameters of G have been established.

Keywords: Graph, Litact Graph, Split Domination Number, Regular Domination Number, Split Regular Domination Number

References

  1. Lakshmi AR, Majeed A, Devi JV. Strong Split Litact Domination in Graphs. International Journal of Recent Technology and Engineering (IJRTE). 2019;8(3):7296–7300. Available from: https://doi.org/10.35940/ijrte.C3924.098319
  2. Mohanapriya A, Renjith P, Sadagopan N. Domination and its variants in split graphs -P versus NPC dichotomy. The Journal of Analysis. 2023;31(1):353–364. Available from: https://dx.doi.org/10.1007/s41478-022-00463-5
  3. Sumathi R, Yamini LDL, . The split domination in arithmetic graphs. International Journal of Engineering, Science and Mathematics. 2019;8(7):22–28. Available from: https://www.indianjournals.com/ijor.aspx?target=ijor:ijesm&volume=8&issue=7&article=002
  4. Amutha S, Prabha KS, Anbazhagan N, Gomathi SS, Cangul IN. On α -Split Domination in Graphs. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences. 2022;92(4):593–597. Available from: https://dx.doi.org/10.1007/s40010-022-00778-9
  5. Mallinath KS, S. Split Domination in Lict Subdivision Graph of a Graph. European Chemical Bulletin. 2023;12(Special Issue 4):7719–7726. Available from: https://www.eurchembull.com/uploads/paper/582189fa258bab7b63d328151057b24a.pdf
  6. Lakshmi R, Majeed A, Devi JV. Split Litact Domination in Graphs. International Journal of Future Generation Communication and Networking. 2020;13(3):3642–3648. Available from: http://sersc.org/journals/index.php/IJFGCN/article/view/30754/17077
  7. Suja K, Vishwanathan K. Split domination of some special graph. In: 2ND INTERNATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS: ICMTA2021, AIP Conference Proceedings. (Vol. 2516, Issue 1) AIP Publishing. 2022.
  8. Lakshmi AR, Vani M, Majeed A. Inverse litact domination in graphs. Materials Today: Proceedings. 2022;65(Part 8):3552–3557. Available from: https://dx.doi.org/10.1016/j.matpr.2022.06.147

Copyright

© 2024 Shankarajyothi & Reddy.  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)

DON'T MISS OUT!

Subscribe now for latest articles and news.