On Constructing Regular Distance-Preserving Graphs
Combinatorics
2014-05-08 v1
Abstract
Let G be a simple, connected graph on n vertices. Let d_G(u,v) denote the distance between vertices u and v in G. A subgraph H of G is isometric if d_H(u,v)=d_G(u,v) for every u,v in V(H). We say that G is a distance-preserving graph if G contains at least one isometric subgraph of order k for every k, 1\le k\le n. In this paper we construct regular distance-preserving graphs of all possible orders and degrees of regularity. By modifying the Havel-Hakimi algorithm, we are able to construct distance preserving graphs for certain other degree sequences as well. We include a discussion of some related conjectures which we have computationally verified for small values of n.
Cite
@article{arxiv.1405.1713,
title = {On Constructing Regular Distance-Preserving Graphs},
author = {Abdol-Hossein Esfahanian and Ronald Nussbaum and Dennis Ross and Bruce E. Sagan},
journal= {arXiv preprint arXiv:1405.1713},
year = {2014}
}
Comments
9 pages, 4 figures, 2 tables