Power domination in Mycielskian of spiders
The power domination problem in graphs consists of finding a minimum set of vertices [Formula: see text] that monitors the entire graph G governed by two ‘monitoring rules’- domination and propagation. A set [Formula: see text] is a power dominating set (PDS) if it can monitor all vertices of G. The...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2022-05-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2022.2082900 |
| Summary: | The power domination problem in graphs consists of finding a minimum set of vertices [Formula: see text] that monitors the entire graph G governed by two ‘monitoring rules’- domination and propagation. A set [Formula: see text] is a power dominating set (PDS) if it can monitor all vertices of G. The minimum cardinality of a PDS of G is called the power domination number, [Formula: see text], of G. In this paper, we study the power domination problem in Mycielskian of spiders. For a spider T, we have [Formula: see text] and [Formula: see text]. We characterize spiders, T, for which [Formula: see text] and [Formula: see text] |
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| ISSN: | 0972-8600 2543-3474 |