| Issue |
RAIRO-Oper. Res.
Volume 56, Number 5, September-October 2022
|
|
|---|---|---|
| Page(s) | 3367 - 3371 | |
| DOI | https://doi.org/10.1051/ro/2022150 | |
| Published online | 14 September 2022 | |
A note on the double domination number in maximal outerplanar and planar graphs
1
School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Penang, Malaysia
2
Department of Mathematics, Shahed University, Tehran, Iran
* Corresponding author: n.jafarirad@gmail.com
Received:
2
July
2021
Accepted:
16
August
2022
In a graph, a vertex dominates itself and its neighbors. A subset S of vertices of a graph G is a double dominating set of G if S dominates every vertex of G at least twice. The double domination number γ×2(G) of G is the minimum cardinality of a double dominating set of G. In this paper, we prove that the double domination number of a maximal outerplanar graph G of order n is bounded above by n+k/2, where k is the number of pairs of consecutive vertices of degree two and with distance at least 3 on the outer cycle. We also prove that γ×2(G) ≤ 5n/8 for a Hamiltonian maximal planar graph G of order n ≥ 7.
Mathematics Subject Classification: 05C69
Key words: Domination / double domination / maximal outerplanar graph / Hamiltonian maximal planar graph
© The authors. Published by EDP Sciences, ROADEF, SMAI 2022
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