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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.
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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
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