Some results related to the Kulli-Sigarkanti conjecture

dc.contributor.authorKeith Driscoll
dc.contributor.authorElliot Krop
dc.description.abstractWe 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. \\
dc.titleSome results related to the Kulli-Sigarkanti conjecture
dc.typeJournal Article, Academic Journal
dcterms.bibliographicCitationCongressus Numerantium/Utilitas Mathematica Publishing, Inc. 231, 137-142, (December 2018)