Hamiltonicity on Enhanced Extended Fibonacci Cube

Enhanced Hypercube (EQ) is a computer network interconnect topology that has many advantages. But among the many advantages, EQ has some drawbacks that is in line with the increasing network size, the number of vertices increases exponentially. Extended Fibonacci Cube {EFC) is an interconnected network topology developed to overcome weaknesses in EQ related to number of vertices. E FC is developed following the Fibonacci number pattern. This paper introduces a new interconnect network topology named Enhanced Extended Fibonacci Cube (E2FC) developed from E FC to overcome weaknesses in EQ while also increasing the advantages already possessed by EFC. In the previous research, the enumeration formula of vertex number, number of edges, number of squares and size of diameter from E1FC. In this paper will be shown the important nature of a computer network that is the nature of Hamiltonicity. The existence of this propertiy is important because it is related to the ability of a network to send messages efficiently. In this paper it is shown that E2.FC is a Hamiltonian graph. Proof analysis using binary string combinatoric method.