I finally found the name of this almost leafless branching succulent from the Euphorbiaceae Family. Commonly known as Finger Tree, Firestick Tree, Indian Tree Spurge, Milk Bush, Naked Lady, Pencil Cactus etc, this succulent grows very well in semi-arid areas.
The other synonyms include E. rhipsaloides and E. viminalis. A few links are provided below: