Unique Minimum Semipaired Dominating Sets in Trees
Let G be a graph with vertex set V. 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 is the minimum cardinality of a semipaired dominating set of G. We characterize the trees having a unique minimum semipaired dominating set. We also determine an upper bound on the semipaired domination number of these trees and characterize the trees attaining this bound.
Haynes, Teresa W.; and Henning, Michael A.. 2020. Unique Minimum Semipaired Dominating Sets in Trees. Discussiones Mathematicae - Graph Theory. https://doi.org/10.7151/dmgt.2349 ISSN: 1234-3099