Structural and Algorithmic Analysis of Domination Parameters in Complex Graph Networks

Author(s)	Mr. Sarang Dharmendra Balshete
Country	India
Abstract	This investigation proposes a structural and algorithmic approach to analyze domination metrics in complex graph networks. Ten benchmark graphs, namely the complete graph, path graph, cycle graph, star graph, wheel graph, grid graph, Erdős–Rényi graphs, Barabási–Albert graphs and Petersen graph were studied with respect to domination form, total domination form and connected domination form. Both exact ILP methodology and greedy heuristic technique were used to test for efficiency in computation. The study revealed that domination forms were dependent on the network structure whereby denser and hub-dominated graphs had lesser dominating number of vertices in comparison to sparse graphs. The ILP produced optimal solutions at the expense of time. The greedy approach scored sub-millisecond time with an approximation ratio ranging from 1.00 to 1.33. Network density and average degree were negatively correlated to activity.
Keywords	Graph domination; Complex networks; Domination parameters; Integer Linear Programming; Greedy heuristic; Network topology; Computational optimization.
Field	Computer > Network / Security
Published In	Volume 8, Issue 5, September-October 2026
Published On	2026-09-11

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