Some results related to the Kulli-Sigarkanti conjecture
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Authors
Keith Driscoll
Elliot Krop
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Journal Article, Academic Journal
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Abstract
We give two proof of the following type bound: for any graph $G$, if $\gamma^{-1}(G)$ is the inverse domination number of $G$ and $\alpha(G)$ is the independence number of $G$, then there exists constants $c$ and $d$ so that $\gamma^{-1}(G)\le c\alpha(G)-d$. In particular, we show that under the same conditions, $\gamma^{-1}(G)\le \alpha(G)+\gamma(G)-2$. Furthermore, we prove that the inequality $\gamma^{-1}(G)\le \alpha(G)$ is true for all $G$, if it is true for the family of graphs which are inverse domination vertex critical, inverse domination critical with respect to edge contraction, but not inverse domination edge critical. \\