Hypercube is a popular and more attractive interconnection networks. The attractive properties of hypercube caused the derivation of more variants of hypercube. In this paper, we have proposed two variants of hypercube which was called as "Fractal Cubic Network Graphs", and we have investigated the Hamiltonian-like properties of Fractal Cubic Network Graphs FCNG(r)(n). Firstly, Fractal Cubic Network Graphs FCNG(r)(n) are defined by a fractal structure. Further, we show the construction and characteristics analyses of FCNG(r)(n) where r = 1 or r = 2. Therefore, FCNG(r)(n) is a Hamiltonian graph which is obtained by using Gray Code for r = 2 and FCNG(1)(n) is not a Hamiltonian Graph. Furthermore, we have obtained a recursive algorithm which is used to label the nodes of FCNG(2)(n). Finally, we get routing algorithms on FCNG(2)(n) by utilizing routing algorithms on the hypercubes. (C) 2015 Karabuk University. Production and hosting by Elsevier B.V.