Some results on neighbourhood highly irregular graphs. (Q2881273)
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scientific article; zbMATH DE number 6021496
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some results on neighbourhood highly irregular graphs. |
scientific article; zbMATH DE number 6021496 |
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3 April 2012
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irregular graph
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highly irregular graph
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neighborhood highly irregular graph
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0.91161776
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0.89068615
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0.88395554
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Some results on neighbourhood highly irregular graphs. (English)
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A connected simple graph \(G = (V,E)\) is said to be a neighborhood highly irregular graph if for any vertex \(v \in V\), any two distinct vertices in the open neighborhood of \(v\) have distinct closed neighborhood sets. The main result of the paper is as follows: The smallest order of a neighborhood highly irregular graph with clique number \(n\) is \(n + \left \lceil \log _2 n \right \rceil \).
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