The Paired-domination and the Upper Paired-domination Numbers of Graphs
نویسندگان
چکیده
In this paper we continue the study of paired-domination in graphs. A paired–dominating set, abbreviated PDS, of a graph G with no isolated vertex is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number of G, denoted by γp(G), is the minimum cardinality of a PDS of G. The upper paired–domination number of G, denoted by Γp(G), is the maximum cardinality of a minimal PDS of G. Let G be a connected graph of order n ≥ 3. Haynes and Slater in [Paired-domination in graphs, Networks 32 (1998), 199–206], showed that γp(G) ≤ n−1 and they determine the extremal graphs G achieving this bound. In this paper we obtain analogous results for Γp(G). Dorbec, Henning and McCoy in [Upper total domination versus upper paired-domination, Questiones Mathematicae 30 (2007), 1–12] determine Γp(Pn), instead in this paper we determine Γp(Cn). Moreover, we describe some families of graphs G for which the equality γp(G) = Γp(G) holds.
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