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Let G=(V,E) be a connected graph with ‘n’ vertices. A HAMILTONIAN CYCLE is a round trip path along ‘n’ edges of G that visits every vertex once and returns to its starting position.

If the Hamiltonian cycle begins at some vertex V1 belongs to G and the vertices of G are visited in the order of V1,V2…….Vn+1,then the edges (Vi,Vi+1) are in E,1n, and the Vi are distinct except for V1 and Vn+1 which are equal.