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The research aims to address the Graph Reconstruction Conjecture using a novel geometric framework known as Wave-Point Geometry.

June 6, 2026Open Access

Graph Reconstruction via Wave-Point Geometry

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The research aims to address the Graph Reconstruction Conjecture using a novel geometric framework known as Wave-Point Geometry.
Introduces foundational theory of Wave-Point Geometry encompassing metrics and curvature flows.
Applies the framework to analyze the effects of deleting a vertex in graph structures.
Establishes the Gap Theorem and defines a Score Function to identify neighborhoods from vertex-deleted subgraphs.
Demonstrates unique curvature distortion patterns induced by single vertex deletion.
Proves that neighborhoods can be identified from subgraphs with one vertex removed.
Provides a measure-theoretic proof of the Reconstruction Conjecture for almost all graphs.

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Novel framework demonstrates true identification of graphs from vertex-deleted subgraphs, suggesting new insights in graph theory.

Ren Matsuoka (2026) studied this question.

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