A Class of Graph-Geodetic Distances Generalizing the Shortest-Path and the Resistance Distances
Combinatorics
2011-01-25 v8 Discrete Mathematics
Metric Geometry
Abstract
A new class of distances for graph vertices is proposed. This class contains parametric families of distances which reduce to the shortest-path, weighted shortest-path, and the resistance distances at the limiting values of the family parameters. The main property of the class is that all distances it comprises are graph-geodetic: if and only if every path from to passes through . The construction of the class is based on the matrix forest theorem and the transition inequality.
Keywords
Cite
@article{arxiv.0810.2717,
title = {A Class of Graph-Geodetic Distances Generalizing the Shortest-Path and the Resistance Distances},
author = {Pavel Chebotarev},
journal= {arXiv preprint arXiv:0810.2717},
year = {2011}
}
Comments
14 pages. Discrete Applied Mathematics