Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Constructing Regular Distance-Preserving Graphs   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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The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
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The categories of this paper are: stat