Maximal outerplanar graphs with semipaired domination number double the domination number

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 pair dominating set S of G is a dominating set of G such that G[S] has a perfect matching. Further, 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 domination number γ(G) is the minimum cardinality of a dominating set of G. Similarly, the paired (semipaired) domination number γpr(G) (γpr2(G)) is the minimum cardinality of a paired (semipaired) dominating set of G. It is known that for a graph G, γ(G)≤γpr2(G)≤γpr(G)≤2γ(G). In this paper, we characterize maximal outerplanar graphs G satisfying γpr2(G)=2γ(G). Hence, our result yields the characterization of maximal outerplanar graphs G satisfying γpr(G)=2γ(G).