On two problems about (0, 2)-graphs and interval-regular graphs (Q2713628)
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scientific article; zbMATH DE number 1602760
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On two problems about (0, 2)-graphs and interval-regular graphs |
scientific article; zbMATH DE number 1602760 |
Statements
10 June 2001
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\((0,2)\)-graph
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interval-regular graph
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interval-monotone graph
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On two problems about (0, 2)-graphs and interval-regular graphs (English)
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A \((0,2)\)-graph is a connected graph in which any two distinct vertices have either no common neighbour, or exactly two. An interval-regular graph is a graph in which for any two vertices \(u,v\) the number of neighbours of \(u\) lying on a shortest \((u,v)\)-paths is equal to the distance between \(u\) and \(v\). Graph operations preserving the property of being a \((0,2)\)-graph are studied. The results enable to construct non-vertex-transitive \((0,2)\)-graphs and to construct a family of regular interval-regular graphs which are not interval-monotone. The latter construction disproves a weaker version of a conjecture by H. M. Mulder.
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