Unique Minimum Semipaired Dominating Sets in Trees

Creator(s)

Teresa W. Haynes, East Tennessee State UniversityFollow
Michael A. Henning, University of Johannesburg

Document Type

Article

Publication Date

1-1-2020

Description

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.

Citation Information

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