Connected Roman Hop Dominating Functions in Graphs (European Journal of Pure and Applied Mathematics, 2025)
Let $G$ be a connected graph. A hop Roman dominating function $f:V(G)→ \{0,1,2\}$ 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 $ω_G^{cRh}(f)=\sum_{v\in V(G)}f(v)$ and the minimum weight among all connected hop Roman dominating functions on $G$, denoted $γ_{cRh}(G)$, 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.
Keywords: Connected Hop Domination, Roman Domination