Abstract: We considered the extreme problem of the Randic energy of unicyclic graphs C_g∪S_t composed of sticking a star graph S_t at a certain vertex on the circle C_g. Using the definition and properties of the Randic energy, and combined with graph transformations, we found the graph that obtained the minimum Randic energy in this class of unicyclic graphs C_g∪S_t.

Key words: Randic energy, graph transformation, unicyclic graph, characteristic polynomial