Graphs With Large Semipaired Domination Number
Let G be a graph with vertex set V and no isolated vertices. A subset S ⊆ V is a semipaired dominating set of G if every vertex in V \ S is adjacent to a vertex in S and S can be partitioned into two element subsets such that the vertices in each subset are at most distance two apart. The semipaired domination number γ pr2 (G) is the minimum cardinality of a semipaired dominating set of G. We show that if G is a connected graph G of order n ≥ 3, then γ pr2 (G) ≤ 32 n, and we characterize the extremal graphs achieving equality in the bound.
Haynes, Teresa W.; and Henning, Michael A.. 2019. Graphs With Large Semipaired Domination Number. Discussiones Mathematicae - Graph Theory. Vol.39(2). 655-657. https://doi.org/10.7151/dmgt.2143 ISSN: 1234-3099