A Note on the Fair Domination Number in Outerplanar Graphs
For ≥ 1, a -fair dominating set (or just FD-set), in a graph is a dominating set such that | ) ∩ | = for every vertex − . The -fair domination number of , denoted by ), is the minimum cardinality of a FD-set. A fair dominating set, abbreviated FD-set, is a FD-set for some integer ≥ 1. The fair domin...
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| Veröffentlicht in: | Discussiones Mathematicae. Graph Theory 2020-11, Vol.40 (4), p.1085-1093 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | For
≥ 1, a
-fair dominating set (or just
FD-set), in a graph
is a dominating set
such that |
) ∩
| =
for every vertex
−
. The
-fair domination number of
, denoted by
), is the minimum cardinality of a
FD-set. A fair dominating set, abbreviated FD-set, is a
FD-set for some integer
≥ 1. The fair domination number, denoted by
), of
that is not the empty graph, is the minimum cardinality of an FD-set in
. In this paper, we present a new sharp upper bound for the fair domination number of an outerplanar graph. |
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| ISSN: | 1234-3099 2083-5892 |
| DOI: | 10.7151/dmgt.2157 |