Semipaired domination in maximal outerplanar graphs

Total domination in plane triangulations

“…In [17], Lemanska et al presented an alternative proof of this last result. The reader is referred to [3,2,4,12,16] for other results in MOPs related to some variants of the domination concept.…”

Unique minimum semipaired dominating sets in trees

“…In other words, the vertices in the dominating set S can be partitioned into 2-sets such that if {u, v} is a 2-set, then uv ∈ E(G) or the distance between u and v is 2. We say that u and v are paired, and that u and v are partners with respect to the resulting semi-matching consisting of the pairings of vertices of S. The semipaired domination number, denoted by γ pr2 (G), is the minimum cardinality of a semi-PD-set of G. We call a semi-PD-set of G of cardinality γ pr2 (G) a γ pr2 -set of G. Semipaired domination was introduced in [11] and studied, for example, in [12,13,[19][20][21]. From the definitions, we observe the following.…”

Connected domination in maximal outerplanar graphs

“…Li et al [15] improved the result by showing that γ(G) ≤ n+t 4 , where t is the number of pairs of consecutive 2-degree vertices with distance at least 3 on the outer cycle. For results on other types of domination in maximal outerplanar graphs, we refer the reader to [1,3,7,8,12,14,19,20].…”