Biharmonic distance of graphs

2021/10/06 by Yulong Wei, Ronghua Li, Wei, Yulong +3
Computer Science · Engineering · #3D Shape Modeling and Analysis #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2110.02656

openalex publication_date 2021/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Lipman et al. [ACM Transactions on Graphics 29 (3) (2010), 1--11] introduced the concept of biharmonic distance to measure the distances between pairs of points on a 3D surface. Biharmonic distance has some advantages over resistance distance and geodesic distance in some realistic contexts. Nevertheless, limited work has been done on the biharmonic distance in the discrete case. In this paper, we give some characterizations of the biharmonic distance of a graph. Some basic mathematical properties of biharmonic distance and biharmonic index are established.

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