Bounds for the connected domination number of maximal outerplanar graphs
A dominating set of a graph G is a set S⊆V(G) such that every vertex in G is either in S or adjacent to a vertex in S. A dominating set S is a connected dominating set if the subgraph of G induced by S is connected. The minimum cardinality of a connected dominating set of G is the connected dominati...
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| Vydáno v: | Discrete Applied Mathematics Ročník 320; s. 235 - 244 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier B.V
30.10.2022
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| Témata: | |
| ISSN: | 0166-218X, 1872-6771 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | A dominating set of a graph G is a set S⊆V(G) such that every vertex in G is either in S or adjacent to a vertex in S. A dominating set S is a connected dominating set if the subgraph of G induced by S is connected. The minimum cardinality of a connected dominating set of G is the connected domination number, denoted by γc(G). Zhuang showed that γc(G) of a maximal outerplanar graph G is bounded by min{⌊n+k2⌋−2,⌊2(n−k)3⌋} (Zhuang, 2020), where k is the number of 2-degree vertices in G. In this paper, we give an algorithm for finding a connected dominating set of maximal outerplanar graphs and get an upper bound γc(G)≤⌊n−k+x2⌋, where x is a counter in the algorithm and x≤k−2. As a corollary, the result that γc(G)≤⌊n−22⌋ for a maximal outerplanar G is gotten directly. This results is better than the above known bound for 3<k<n+64. In addition, we complement some analysis with simulations to evaluate the advantages of our results. |
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| ISSN: | 0166-218X 1872-6771 |
| DOI: | 10.1016/j.dam.2022.05.024 |