Upper bounds for inverse domination in graphs

Authors

Elliot Krop, Clayton State UniversityFollow
Jessica McDonald, Auburn UniversityFollow
Gregory J. Puleo, Auburn UniversityFollow

Abstract

In any graph G, the domination number \gamma(G) is at most the independence number \alpha(G). The Inverse Domination Conjecture says that, in any isolate-free G, there exists pair of vertex-disjoint dominating sets D, D' with |D|=\gamma(G) and |D'| \leq \alpha(G). Here we prove that this statement is true if the upper bound \alpha(G) is replaced by \frac{3}{2}\alpha(G) – 1 (and G is not a clique). We also prove that the conjecture holds whenever \gamma(G)\leq 5 or |V(G)|\leq 16.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Krop, Elliot; McDonald, Jessica; and Puleo, Gregory J. (2021) "Upper bounds for inverse domination in graphs," Theory and Applications of Graphs: Vol. 8: Iss. 2, Article 5.
DOI: 10.20429/tag.2021.080205
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol8/iss2/5