• Mahesh S A
• M Manjunatha
• Puttaswamy
• Karthik K R

Graph theory is essential in several scientific and industrial fields, with dominance parameters being a significant focus because to its relevance in network optimisation, social network research, and resource allocation. Conventional dominance models, like Total Domination (TD) and Independent Domination (ID), emphasise fundamental node coverage and independent selection but neglect to integrate structural, probabilistic, and spectral characteristics of networks. This paper presents the Hybrid Multi-Dimensional Domination (HMD) model, which incorporates three essential components: Structural Domination Component (SDC), Probabilistic Influence Component (PIC), and Algebraic Domination Component (ADC). On the basis of these mathematical models, the HMD model provides a better estimate of node influence and network resilience. Comparison experiments of HMD with TD and ID confirm its excellence in terms of coverage ratio, average node influence score, computational complexity, and network resilience against failure. The experiments show that the HMD model provides a resilient approach to dominance analysis, and graph theory becomes increasingly applicable to real-world, complex networks.

Total Domination, Independent Domination, Structural Domination Component (SDC), Probabilistic Influence Component (PIC), and Algebraic Domination Component (ADC), Hybrid Multi-Dimensional Domination (HMD).

"Exploration of Novel Domination Parameters in Graph Theory", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.12, Issue 2, page no.d203-d221, February-2025, Available :http://www.jetir.org/papers/JETIR2502323.pdf

"Exploration of Novel Domination Parameters in Graph Theory", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.12, Issue 2, page no. ppd203-d221, February-2025, Available at : http://www.jetir.org/papers/JETIR2502323.pdf