Total vertex covers (Q2839639)
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scientific article; zbMATH DE number 6187547
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Total vertex covers |
scientific article; zbMATH DE number 6187547 |
Statements
12 July 2013
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connected graph
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vertex cover
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total vertex cover
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dominating set
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total dominating set
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extremal graph
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Total vertex covers (English)
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For a graph \(G\), a subset of vertices \(S\) is said to be a total vertex cover when every vertex has a neighbor in \(S\) and every edge has at least one endpoint in \(S\). The number of vertices in a smallest total vertex cover is called the total vertex cover number of \(G\). In this paper upper and lower bounds concerning this parameter in connected graphs are developed. Extremal graphs related to some such bounds are also described.
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