Connected Roman Hop Dominating Functions in Graphs
Alkajim A. Aradais, Jerry Boy Cariaga, Sergio Canoy · European Journal of Pure and Applied Mathematics · 2025
Let $G$ be a connected graph. A hop Roman dominating function $f:V(G)\to \{0,1,2\}$ is a connected hop Roman dominating function (CHRDF) on $G$ if the set $\{u\in V(G): f(u) eq 0\}$ induces a connected subgraph of $G$. The of weight of a CHRDF f is given by $\omega_G^{cRh}(f)=\sum_{v\in V(G)}f(v)$ and the minimum weight among all connected hop Roman dominating functions on $G$, denoted $\gamma_{cRh}(G)$, is the connected hop Roman domination number of $G$. In this paper, we show that the parameter lies between the connected hop domination number of $G$ and twice this number. We characterize the graphs that attain small values of the parameter and determine the connected hop Roman dominationnumber of some graphs.