(untitled) (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 {uV(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)=_vV(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 domination number of some graphs.