Harary圖上的 k元全支配問題

In this report, we are concerned with the 2-tuple total domination number $\gamma_{\times2,t}(H_{m, n})$ of Harary graphs $H_{m, n}$, where $m$ is odd. We complete the analysis for $m=3$, and give some result for $m=5$. For $m$ large enough, we show that there exists $m$-regular graphs whose 2-tuple total domination number matches the lower bound of $\lceil 2n/m\rceil$.