Hang Chen

Tight bounds for generalized power domination in regular graphs

Dorbec et al. [SIAM J. Discrete Math., 27 (2013)] conjectured that, for all integers $k\geq1$ and $r\geq3$, every connected $r$-regular graph $G$ of order $n$, other than $K_{r,r}$, satisfies $\gamma_{P,k}(G)\leq n/(r+1)$. After disproving this conjecture, Chen et al.[Graphs Combin., 38 (2022)] proposed a corresponding...