• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

Year: 2024, Volume: 17, Issue: 13, Pages: 1315-1322

Original Article

Lict k-Domination in Graphs

Received Date:09 December 2023, Accepted Date:01 March 2024, Published Date:22 March 2024


Objectives: In this study, we find lict -domination number of various types of graphs. Methods: Let be any graph, a set is said to be an -dominating set of lict graph if every vertex is dominated by at least vertices in , that is . The Lict -domination number is the minimum cardinality of -dominating set of . Findings: This study is centered on the lict -domination number of the graph and developed its relationship with other different domination parameters. Novelty: This study introduces the concept of “Lict -Domination in Graphs”. It obtains many bounds on in terms of vertices, edges, and other different parameters of .

Keywords: Domination number, k-domination number, Lict graph, Lict k-domination number, Total domination number, Independent domination number


  1. Harary F. Graph Theory. Reading, Massachusetts, USA. Adison Wesley. 1969.
  2. Hoppen C, Mansan G. Total Domination in Regular Graphs. Electronic Notes in Theoretical Computer Science. 2019;346:523–533. Available from: https://doi.org/10.1016/j.entcs.2019.08.046
  3. Cho E, Choi I, Park B. On independent domination of regular graphs. Journal of Graph Theory. 2023;103(1):159–170. Available from: https://doi.org/10.1002/jgt.22912
  4. Muddebihal MH, Baburao G. Weak domination in lict graphs. International Journal of Computer Applications. 2020;176(11):13–16. Available from: https://www.ijcaonline.org/archives/volume176/number11/muddebihal-2020-ijca-920023.pdf
  5. Aejaz S, Muddebihal, Akka DG. Set-domination in lict graphs. Far East Journal of Mathematical Sciences (FJMS). 2020;125(1):49–58. Available from: http://dx.doi.org/10.17654/MS125010049
  6. 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
  7. Mallinath KS, S. Lict subdivision connected domination in graphs. Turkish Journal of Computer and Mathematics Education. 2021;12(14):4040–4049. Available from: https://doi.org/10.17762/turcomat.v12i14.11091
  8. Bermudo S, Hernandez-Gomez JC, Sigarreta JM. Total k-domination in strong product graphs. Discrete Applied Mathematics. 2019;263(C):51–58. Available from: https://doi.org/10.1016/j.dam.2018.03.043
  9. Ekinci GB, Bujtás C. Bipartite graphs with close domination and k-domination numbers. Open Mathematics. 2020;18(1):873–885. Available from: http://dx.doi.org/10.1515/math-2020-0047
  10. Martinez AC. Some new results on the k-tuple domination number of graphs. RAIRO-Operations Research. 2022;56(5):3491–3497. Available from: https://doi.org/10.1051/ro/2022159
  11. Carballosa W, Wisby J. Total k-domination in Cartesian product of complete graphs. Discrete Applied Mathematics. 2023;337:25–41. Available from: https://doi.org/10.1016/j.dam.2023.04.008
  12. Volkmann AL. A bound on the k-domination number of a graph. Czechoslovak Mathematical Journal. 2010;60(1):77–83. Available from: https://dml.cz/handle/10338.dmlcz/140550
  13. Haynes TW, Hedetniemi ST, Henning MA. Topics in Domination in Graphs, Developments in Mathematics . (Vol. 64) Springer Cham. 2020.
  14. Rajasekharaiah GV, Murthy UP, . Secure domination in lict graphs. Open Journal of Mathematical Science. 2018;2(1):134–145. Available from: https://pisrt.org/psrpress/j/oms/2018/1/11/secure-domination-in-lict-graphs.pdf
  15. Kulli VR. Theory of Domination in Graphs. (pp. 1-284) Vishwa International Publications. 2010.
  16. Girish VR, Usha P. Total domination in lict graph. International Journal of Mathematical Combinatorics. 2014;1:19–27. Available from: https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=74fbdf2d695066d82e1a2d11593a998f245b4f69


© 2024 Gade & Vyavahare. 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)


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