The Interplay Between Domination and Separation in Graphs

2026-01-28

Latin-American Algorithms, Graphs and Optimization Symposium

AI Summary

This study investigates vertex identification in graphs based on dominating sets, with a focus on distinguishing any pair of vertices through separation properties. It systematically characterizes the computational complexity boundaries of finding minimum separating sets under four separation notions: location, closed, open, and total separation. Employing graph-theoretic modeling, complexity analysis, and combinatorial optimization, the work establishes intrinsic connections between these separation properties and various domination codes. A key contribution is the discovery of a duality between separation properties in a graph and its complement: location and total separation are invariant under complementation, while closed and open separation are dual to each other—each corresponding to the other in the complement graph.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Models for Web evolution

Problem

• domination
• separation
• graph identification
• codes
• complementation

Innovation

• domination
• separation
• graph codes
• complementation
• complexity