Edge lifting and Roman domination in graphs

Let G be a graph, and let uxv be an induced path centered at x. An edge lift defined on uxv is the action of removing edges ux and vx while adding the edge uv to the edge set of G. In this paper, we initiate the study of the effects of edge lifting on the Roman domination number of a graph, where various properties are established. A characterization of all trees for which every edge lift increases the Roman domination number is provided. Moreover, we characterize the edge lift of a graph decreasing the Roman domination number, and we show that there are no graphs with at most one cycle for which every possible edge lift can have this property.