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arXiv · 1405.1713

On Constructing Regular Distance-Preserving Graphs

Abdol-Hossein Esfahanian·Ronald Nussbaum·Dennis Ross·Bruce E. Sagan
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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.

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Abdol-Hossein Esfahanian, Ronald Nussbaum, Dennis Ross, Bruce E. Sagan. 2014-05-07. On Constructing Regular Distance-Preserving Graphs. https://arxiv.org/abs/1405.1713

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