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abstract: |
    A fair dominating set in a graph $G$ (or FD-set) is a dominating set $S$ such that all vertices not in $S$ are dominated by the same number of vertices from $S$; that is, every two vertices not in $S$ have the same number of neighbors in $S$. The fair domination number, ${{\rm fd}}(G)$, of $G$ is the minimum cardinality of a FD-set. We present various results on the fair domination number of a graph. In particular, we show that if $G$ is a connected graph of order $n \ge
    3$ with no isolated vertex, then ${{\rm fd}}(G) \le n - 2$, and we construct an infinite family of connected graphs achieving equality in this bound. We show that if $G$ is a maximal outerplanar graph, then ${{\rm fd}}(G) < 17n/19$. If $T$ is a tree of order $n \ge 2$, then we prove that ${{\rm fd}}(T) \le n/2$ with equality if and only if $T$ is the corona of a tree.
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[Fair Domination in Graphs]{}\

[2]{}

Yair Caro\
[Dept. of Mathematics and Physics\
University of Haifa-Oranim\
Tivon 36006, Israel\
yacaro@kvgeva.org.il]{}

Adriana Hansberg\
[Dept. de Matemàtica Aplicada III\
UPC Barcelona\
08034 Barcelona, Spain\
adriana.hansberg@upc.edu]{}\

Michael Henning\
