Isometric embeddings of graphs into Riemannian manifolds

2018/04/19 by Shiquan Ren, Ren, Shiquan · 1 citation
Computer Science · Engineering · Mathematics · #3D Shape Modeling and Analysis #FOS: Mathematics #Metric Geometry (math.MG) #Morphological variations and asymmetry #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1804.07136

openalex publication_date 2018/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An isometric embedding of a graph into a metric space is an embedding of the vertices such that the smallest number of edges connecting any two vertices equals to the distance in the metric space between the images. In this paper, we study isometric embeddings of graphs into Riemannian manifolds. We give some classifications of graphs that can be isometrically embedded into certain Riemannian manifolds.

Cited by

• Design Principles for Realizable Discrete Surface Embeddings in Physical Systems

Related

• Graph embeddings into Hamming spaces
• Forbidden Four Cycle, Star Graphs and Isometric Embeddings
• On the Structure of Isometrically Embeddable Metric Spaces
• Isometrische Einbettung von geschlossenen Riemannschen Mannigfaltigkeiten
• Embeddings of Grassmann graphs