EXPLORING THE IMPACT OF DOMINATION IN GRAPH STRUCTURES: A COMPREHENSIVE STUDY

Authors

  • Dr. Nanda S Warad Associate Professor, Department of Mathematics, Government First Grade College, Kembhavi
  • Faimida Begum Assistant Professor, Department of Mathematics, Government First Grade College, Humnabad

DOI:

https://doi.org/10.29121/shodhkosh.v5.i6.2024.2356

Keywords:

Graph Domination, Total Domination, Independent Domination, Domination Number, Network Optimization, Algorithmic Complexity

Abstract [English]

Graph domination is a key concept in graph theory, with wide-ranging applications in network security, social networks, and biological systems. This paper presents a comprehensive study of domination in graph structures, exploring various types of domination such as total domination, independent domination, and connected domination. The study delves into the theoretical foundations of domination, including critical bounds, domination numbers, and their computational complexity. The paper also examines real-world applications, highlighting how domination plays a crucial role in optimizing network communication, sensor placement, and resource management. Additionally, we analyze algorithmic approaches for calculating domination numbers and explore how domination impacts graph connectivity and stability in practical scenarios. The results provide insights into how domination theory can be leveraged to enhance the performance and efficiency of complex networks.

References

Haynes, T. W., Hedetniemi, S. T., & Slater, P. J. (1998). Fundamentals of Domination in Graphs. Marcel Dekker. DOI: https://doi.org/10.1002/(SICI)1097-0037(199810)32:3<199::AID-NET4>3.0.CO;2-F

West, D. B. (2001). Introduction to Graph Theory. Prentice Hall.

Cockayne, E. J., & Hedetniemi, S. T. (1977). Towards a theory of domination in graphs. Networks, 7(3), 247-261. DOI: https://doi.org/10.1002/net.3230070305

Fink, J. F., & Jacobson, M. S. (1985). n-domination in graphs. Graph Theory with Applications to Algorithms and Computer Science, 282-300.

Hedetniemi, S. T., Laskar, R. C., & Fricke, G. H. (1997). Domination in Graphs: Advanced Topics. Marcel Dekker.

Slater, P. J. (1988). Dominating and reference sets in graphs. Journal of Mathematical and Physical Sciences, 22(3), 445-455.

Eubank, S., Guclu, H., Kumar, V. S., et al. (2004). Modelling disease outbreaks in realistic urban social networks. Nature, 429(6988), 180-184. DOI: https://doi.org/10.1038/nature02541

Henning, M. A., & Yeo, A. (2013). Total Domination in Graphs. Springer. DOI: https://doi.org/10.1007/978-1-4614-6525-6

Alon, N., & Spencer, J. H. (2004). The Probabilistic Method. Wiley.

Brešar, B., Klavžar, S., & Rall, D. F. (2011). Domination game and an imagination strategy. SIAM Journal on Discrete Mathematics, 24(3), 979-991. DOI: https://doi.org/10.1137/100786800

Clark, W. E., & Suen, S. (2000). An inequality related to Vizing’s conjecture. Electronic Journal of Combinatorics, 7, R43. DOI: https://doi.org/10.37236/1542

Meir, A., & Moon, J. W. (1975). Relations between packing and covering numbers of a tree. Pacific Journal of Mathematics, 61(1), 225-233. DOI: https://doi.org/10.2140/pjm.1975.61.225

Ore, O. (1962). Theory of Graphs. American Mathematical Society. DOI: https://doi.org/10.1090/coll/038

Goddard, W., & Henning, M. A. (2014). Independent domination in graphs: A survey and recent results. Discrete Mathematics, 313(7), 839-854. DOI: https://doi.org/10.1016/j.disc.2012.11.031

J. A. Bondy & U. S. R. Murty (2008). Graph Theory. Springer. DOI: https://doi.org/10.1007/978-1-84628-970-5

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Published

2024-06-30

How to Cite

Warad, N. S., & Begum, F. (2024). EXPLORING THE IMPACT OF DOMINATION IN GRAPH STRUCTURES: A COMPREHENSIVE STUDY. ShodhKosh: Journal of Visual and Performing Arts, 5(6), 1420–1428. https://doi.org/10.29121/shodhkosh.v5.i6.2024.2356