Restrained Regular Domination on a Litact Graph

Authors

  • G. SHANKARAJYOTHI Osmania University
  • G. Upender Reddy

Keywords:

Graph, Litact graph, Regular domination number, Restrained domination number, Restrained regular domination number

Abstract

We present the first research on restrained regular domination, which is a variant of standard domination. Assume that  is a graph. If every vertex in  has at least one neighbour in both  and , and every vertex in  has an identical degree, then a set  is a ‘restrained regular dominating set’, abbreviated RRDS. The least cardinality of all G’s RRDS is the ‘RRD number of G’, represented by . We ascertain the optimal bounds that can be applied to , and we identify the most optimal lower bounds for  and , both  and  are connected. We also characterise those graphs satisfying these bounds.

Downloads

Download data is not yet available.

References

Abiad A, Akbari S, Fakharan M.H, and Mehdizadeh A, A bound for the p-domination number of a graph in terms of its eigenvalue multiplicities, Linear Algebra and its Applications, 658 (2023), 319-330. DOI: 10.1016/j.laa.2022.11.008

Amjadi J, Samadi B, and Volkmann L, Total restrained Roman domination, Communications in Combinatorics and Optimization, 8(3) (2023), 575-587. DOI: 10.22049/CCO.2022.27628.1303

Babak Samadi, Morteza Alishahi, Iman Masoumi, and Doost Ali Mojdeh, Restrained Italian Domination in Graphs, RAIRO Operations Research, 55 (2021) 319-332. DOI: 10.1051/ro/2021022

Barack Z.Z, Sugeng K.A, Semaničová-Feňovčíková A, and Bača M, Modular irregularity strength of the corona product of graphs, Discrete Mathematics Letters, 13 (2024), 111-116. DOI: 10.47443/dml.2024.041

Bärnkopf P, Nagy Z.L, and Paulovics Z, A Note on Internal Partitions: The 5-Regular Case and Beyond, Graphs and Combinatorics, 40(36) (2024). DOI:10.1007/s00373-024-02774-9

Borg P, Isolation of Regular Graphs and k-Chromatic Graphs, Mediterranean Journal of Mathematics, 21 (2024). DOI: 10.1007/s00009-024-02680-7

Brešar B, and Henning M.A, Best possible upper bounds on the restrained domination number of cubic graphs, Journal of Graph Theory, 106 (2024), 763-815. DOI: 10.1002/jgt.23095

Burdett R, Haythorpe M, and Newcombe A, Variants of the domination number for flower snarks, Ars Mathematica Contemporanea, 24 (2024). DOI: 10.26493/1855-3974.2710.f3d

Buvaneswari R, and Umamaheswari K, Bondage and non-bondage sets in regular intuitionistic fuzzy graphs, Notes on Intuitionistic Fuzzy Sets, 29(3) (2023), 318-324. DOI: 10.7546/nifs.2023.29.3.318-324

Celart A. Tuble, and Enrico L. Enriquez, Outer-restrained Domination in the Join and Corona of Graphs, International Journal of Latest Engineering Research and Applications, 9(1) (2024), 50-56. http://dx.doi.org/10.56581/IJLERA.9.1.50-56.

Consistente L.F, and Cabahug I.S., Jr, Restrained Global Defensive Alliances in Graphs, European Journal of Pure and Applied Mathematics, 17(3) (2024), 2196-2209. DOI: 10.29020/nybg.ejpam.v17i3.5156

Gerald B. Monsanto, and Helen M. Rara, Resolving Restrained Domination in Graphs, European Journal of Pure and Applied Mathematics, 14(3) (2021), 829-841. http://dx.doi.org/10.29020/nybg.ejpam.v14i3.3985

Hayat S, Khan A, Alenazi M.J.F, and Wang S, ON THE BINARY LOCATING-DOMINATION NUMBER OF REGULAR AND STRONGLY-REGULAR GRAPHS, Journal of Mathematical Inequalities, 17(4) (2023), 1597-1623. DOI: 10.7153/jmi-2023-17-105

Hemalatha NC, Chandrakala SB, Sooryanarayana B, and Vishu Kumar M, Restrained and Total Restrained Domination of Ladder Graphs, Communications in Mathematics and Applications, 14(4) (2023), 1311–1323, http://doi.org/10.26713/cma.v14i4.2569

Hussain R.J, Hussain S.S, Sahoo S, and Pal M, Domination number of complete restrained fuzzy graphs, International Journal of Advanced Intelligence Paradigms, 24(1/2) (2023), 38-48. DOI: 10.1504/ijaip.2023.128073

Ibrahim TA, and Omran AA, Restrained Whole Domination in Graphs, Journal of Physics: Conference Series, 1879(2020), 9-10, DOI:10.1088/1742-6596/1879/3/032029

Jayasekaran C, and Binoja L.G, RELATIVELY PRIME RESTRAINED DETOUR DOMINATION NUMBER OF A GRAPH, Gulf Journal of Mathematics, 16(2) (2024), 291-297. DOI: 10.56947/gjom.v16i2.1844

Kala R, and Nirmala Vasantha TR, Restrained Double Domination Number of a Graph, AKCE International Journal of Graphs and Combinatorics, 5 (1) (2008), 73-82. https://www.semanticscholar.org/paper/Restrained-Double-Domination-Number-of-a-Graph-Kala-Vasantha/05b2f378a46a66ba5eb28c461918b2be48de2221

Mohannad A, and Mojdeh D.A, ON THE TOTAL RESTRAINED DOUBLE ITALIAN DOMINATION, Journal of Algebra and Related Topics, 12(1) (2024), 105-126. DOI: 10.22124/jart.2023.24056.1507

Muddebihal MH, Kalshetti Swati M, Restrained Lict Domination In Graphs, International Journal of Research in Engineering and Technology, 3(5) (2014), http://dx.doi.org/10.15623/ijret.2014.0305145

Nair K.R, and Sunitha M.S, Strong Domination Index in Fuzzy Graphs, Fuzzy Information and Engineering, 16(1) (2024), 1-23. DOI: 10.26599/FIE.2023.9270028

Sarmitha G, Vidyanandini S, and Nayak S.R, Square difference labeling and co-secure domination in middle graph of certain graphs, Journal of Discrete Mathematical Sciences and Cryptography, 27(4) (2024), 1403-1413. DOI: 10.47974/JDMSC-1994

Shi X, Akhoundi M, Talebi A.A, and Mojahedfar M, A Study on Regular Domination in Vague Graphs with Application, Advances in Mathematical Physics, Vol 2023 (2023). DOI: 10.1155/2023/7098134

Sundara Rajan R, Arulanand S, Prabhu S, and Rajasingh I, 2-power domination number for Knödel graphs and its application in communication networks, RAIRO - Operations Research, 57 (2023), 3157-3168. DOI: 10.1051/ro/2023173

Vani M, Abdul Majeed, and Vasundhara Devi J, Edge Litact Domination in graphs, International Journal of Future Generation Communication and Networking, 13 (3) (2020), 3636-3641. http://sersc.org/journals/index.php/IJFGCN/article/view/30753

Volkmann L, Remarks on the restrained Italian domination number in graphs, Communications in Combinatorics and Optimization, 8(1) (2023), 183-191. DOI: 10.22049/CCO.2021.27471.1269

Xia B, Graphical regular representations of (2,p)-generated groups, European Journal of Combinatorics, 124 (2025). DOI: 10.1016/j.ejc.2024.104058

Zainab Yasir Alrikabi, Ahmed A. Omran, and Hassan Jiad Al Hwaeer, Restrained captive domination number, OpenEngineering, 14 (2024), 20220510. https://doi.org/10.1515/eng-2022-0510

Žerovnik J, Rainbow domination regular graphs that are not vertex transitive, Discrete Applied Mathematics, 349 (2024), 144-147. DOI: 10.1016/j.dam.2024.02.013

Zhang J, and Zhu Y, A NOTE ON REGULAR SETS IN CAYLEY GRAPHS, Bulletin of the Australian Mathematical Society, 109 (2024), 1-5. DOI: 10.1017/S0004972723000084

Published

13-08-2025

How to Cite

G. SHANKARAJYOTHI, & G. Upender Reddy. (2025). Restrained Regular Domination on a Litact Graph . Communications in Mathematics and Applications, 16(1). Retrieved from https://www.journals.rgnpublications.com/index.php/cma/article/view/2895

Issue

Vol. 16 No. 1 (2025)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.