Tranquility Domination as a Framework for Stability in Service Networks.

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Bibliographic Details
Title:	Tranquility Domination as a Framework for Stability in Service Networks.
Authors:	M., Viji A.¹ vijiam.am@gmail.com, Kishore, Anjaly¹ anjalykishor@gmail.com, Kuriakose, Reeja² reejaiykulambil@gmail.com
Source:	IAENG International Journal of Computer Science. May2026, Vol. 53 Issue 5, p2021-2031. 11p.
Subjects:	Load balancing (Computer networks), Equilibrium, Graph theory
Abstract:	The conventional notion of domination provides coverage of all vertices in a graph, it ignores how evenly the burden is distributed among the dominating vertices. In many real world situations, it is preferred that no single dominator is overburdened in comparison to others. Uneven distribution of workload can induce system instability, degrade efficiency and increase the risk of failure. Motivated by the need for balanced service distribution, the concept of tranquility domination is introduced. Two dual parameters - Perturbation coefficient and Tranquility coefficient are defined and a conceptual extension of domination termed as Tranquility Domination is proposed. These two parameters measure, respectively, the extent of imbalance and the degree of equilibrium within a dominating configuration. Dominating vertices are interpreted as donors, representing service providers, while dominated vertices are viewed as acceptors, representing service recipients. The donor tranquility and the acceptor tranquility collectively contribute to the overall tranquility of the system. The behaviour of tranquility based domination under various standard graph operations, giving comparisons with traditional domination parameters and many theoretical bounds are also established in the paper. In addition, a distance-k version of tranquility domination is introduced, permitting domination influence to reach vertices within distance k. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	The conventional notion of domination provides coverage of all vertices in a graph, it ignores how evenly the burden is distributed among the dominating vertices. In many real world situations, it is preferred that no single dominator is overburdened in comparison to others. Uneven distribution of workload can induce system instability, degrade efficiency and increase the risk of failure. Motivated by the need for balanced service distribution, the concept of tranquility domination is introduced. Two dual parameters - Perturbation coefficient and Tranquility coefficient are defined and a conceptual extension of domination termed as Tranquility Domination is proposed. These two parameters measure, respectively, the extent of imbalance and the degree of equilibrium within a dominating configuration. Dominating vertices are interpreted as donors, representing service providers, while dominated vertices are viewed as acceptors, representing service recipients. The donor tranquility and the acceptor tranquility collectively contribute to the overall tranquility of the system. The behaviour of tranquility based domination under various standard graph operations, giving comparisons with traditional domination parameters and many theoretical bounds are also established in the paper. In addition, a distance-k version of tranquility domination is introduced, permitting domination influence to reach vertices within distance k. [ABSTRACT FROM AUTHOR]
ISSN:	1819656X