M. Hajian, N. Jafari Rad
A note on the fair domination number in outerplanar graphs
Discussiones Mathematicae Graph Theory
Received 14.11.2017, Revised 02.07.2018, Accepted 02.07.2018, doi: 10.7151/dmgt.2157

For k≥ 1, a k-fair dominating set (or just kFD-set), in a graph G is a dominating set S such that |N(v)∩ S| = k for every vertex v∈V- S. The k-fair domination number of G, denoted by fdk(G), is the minimum cardinality of a kFD-set. A fair dominating set, abbreviated FD-set, is a kFD-set for some integer k≥ 1. The fair domination number, denoted by fd(G), of G that is not the empty graph, is the minimum cardinality of an FD-set in G. In this paper, we present a new sharp upper bound for the fair domination number of an outerplanar graph.
fair domination, outerplanar graph, unicyclic graph