Semipaired domination in maximal outerplanar graphs
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Publication Details
Author list: Henning M.A., Kaemawichanurat P.
Publisher: Springer New York LLC
Publication year: 2019
Volume number: 38
Issue number: 3
Start page: 911
End page: 926
Number of pages: 16
ISSN: 1382-6905
eISSN: 1382-6905
Languages: English-Great Britain (EN-GB)
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Abstract
A subset S of vertices in a graph G is a dominating set if every vertex in V(G) \ S is adjacent to a vertex in S. If the graph G has no isolated vertex, then a semipaired dominating set of G is a dominating set of G with the additional property that the set S can be partitioned into two element subsets such that the vertices in each subset are at most distance two apart. The semipaired domination number γpr 2(G) is the minimum cardinality of a semipaired dominating set of G. Let G be a maximal outerplanar graph of order n with n2 vertices of degree 2. We show that if n≥ 5 , then γpr2(G)≤25n. Further, we show that if n≥ 3 , then γpr2(G)≤13(n+n2). Both bounds are shown to be tight. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
Maximal outerplanar graphs
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