Fractional Star Domination Number of Graphs

P Shanthi; S Amutha; N Anbazhagan; G Uma

doi:10.17485/IJST/v17sp1.111

Article

Fractional Star Domination Number of Graphs

VIEWS 161
PDF 69

Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17sp1.111

Year: 2024, Volume: 17, Issue: Special Issue 1, Pages: 64-70

Original Article

Fractional Star Domination Number of Graphs

P Shanthi¹, S Amutha^2*, N Anbazhagan¹, G Uma¹

¹Department of Mathematics, Alagappa University, Karaikudi, Karaikudi, 630 003, TamilNadu, India
²Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi, 630 003, TamilNadu, India

*Corresponding Author
Email: [email protected]

Received Date:29 August 2023, Accepted Date:05 March 2024, Published Date:28 May 2024

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: Consider a graph is the connected, undirected graph. This study creates a new parameter named the Fractional Star Domination Number (FRSDN), which is denoted by to calculate the minimum weight with the star of all vertices of and the function values of all edges. Methods: This study evaluates the of some standard graphs and bounds by generalizing the value that is provided by the function value of an edges. Findings: This study evaluated on some standard graphs, such as paths, cycles, and the rooted product of paths and cycles. Finally, we obtain some bounds on for some general graphs, as well as the exactness value yielded by them. For any graph without isolated vertices, we have . Novelty: The new parameter FRSDN of is created by combining the fractional dominating function and the star dominating set.

Keywords: Domination Number, Star Domination Number, Fractional Dominating Function, Fractional Domination Number, Fractional Star Domination Number

References

Amutha S, Prabha KS, Anbazhagan N, Shanthi P. Split domination number of divisible dominating graphs. Journal of Discrete Mathematical Sciences and Cryptography. 2021;24(4):997–1006. Available from: https://dx.doi.org/10.1080/09720529.2020.1744813
Raju M, Bhutani KR, Moazzez B, Arumugam S. On -domination in graphs. AKCE International Journal of Graphs and Combinatorics. 2020;17(1):60–64. Available from: https://dx.doi.org/10.1016/j.akcej.2018.07.004
José M, Sigarreta. Total Domination on Some Graph Operators. Mathematics. 2021(3):241. Available from: https://doi.org/10.3390/math9030241
Karunambigai MG, Sathishkumar A. Dominating function in intuitionistic fractional graph. Malaya Journal of Matematik. 2020(4):1653–1660. Available from: https://doi.org/10.26637/MJM0804/0055
Muhiuddin G, Sridharan N, Al-Kadi D, Amutha S, Elnair ME. Reinforcement Number of a Graph with respect to Half-Domination. Journal of Mathematics. 2021;2021:1–7. Available from: https://dx.doi.org/10.1155/2021/6689816
Shanthi P, Amutha S, Anbazhagan N, Prabu SB. Effects on fractional domination in graphs. Journal of Intelligent & Fuzzy Systems. 2023;44(5):7855–7864. Available from: https://dx.doi.org/10.3233/jifs-222999
Alsinai A, Omran AA, Ibrahim TAA, A H. Some Properties of Whole Edge Domination in Graphs. Applied Mathematics & Information Sciences. 2022;16(3):435–440.
Andreatta G, Francesco CD, Giovanni LD, Serafini P. Star partitions on graphs. Discrete Optimization. 2019;33:1–18. Available from: https://dx.doi.org/10.1016/j.disopt.2019.01.002
Zhao Yc, Shan Ef, Miao Ly, Liang Zs. On Signed Star Domination in Graphs. Acta Mathematicae Applicatae Sinica, English Series. 2019;35(2):452–457. Available from: https://dx.doi.org/10.1007/s10255-019-0816-8
Devvrit F, Krim-Yee A, Kumar N, MacGillivray G, Seamone B, Virgile V, et al. Fractional eternal domination: securely distributing resources across a network. Discussiones Mathematicae Graph Theory. 2023. Available from: https://dx.doi.org/10.7151/dmgt.2503
Rey A. Histoire de la science ou histoire des sciences. Brepols Publishers NV. 1930. doi: 10.1484/j.arch.3.369 Available from: https://dx.doi.org/10.1484/j.arch.3.369
Shanthi P, Amutha S, Anbazhagan N, Uma G, Joshi GP, Cho W. Characterization of Fractional Mixed Domination Number of Paths and Cycles. Journal of Mathematics. 2024;2024:1–11. Available from: https://dx.doi.org/10.1155/2024/6619654
Xu B. On edge domination numbers of graphs. Discrete Mathematics. 2005;294(3):311–316. Available from: https://dx.doi.org/10.1016/j.disc.2004.11.008

Copyright

© 2024 Shanthi et al. 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)