In communications network design, network's stability is a very important concept. A network has to be constructed as possible as stable since the stability of a network shows its resistance to vulnerability. Many science and engineering problems can be represented by a network, generalization of which is a graph. Examples of problems that can be represented by a graph include: cyclic sequential circuit, organic molecule structures, mechanical structures, etc. So, a graph can be considered as a model of a communication network. Then, the notions of the graph theory can be used for the stability of a network. In the graph theory, deterministic measures of the stability are used for some parameters of graphs as connectivity, covering number, independence number and dominating number. Then, the stability of a network is defined with deterministic calculation. Today, these parameters take into consideration the neighborhood notion. Now, we consider an edge-accessibility number of a graph. Edge-accessibility is a notion which uses the neighborhood of edges (links). In this paper; we search the edge-accessibility number of a graph. We also give some theorems about the edge-accessibility using the graph operations and design an algorithm which found it with Time Complexity O(n3).
The Fibonacci Cube is an interconnection network that gets many desirable properties that are very important in the network design, network stability and applications. The extended Fibonacci Cube is a new network topology. The vulnerability value of a communication network shows the resistance of the network after the disruption of some centres or connection lines until the communication breakdown. In a network, as the number of centres belonging to sub networks changes, the vulnerability of the network also changes and requires greater degrees of stability or less vulnerability. If the communication network is modelled by graph G, the deterministic measures tend to provide a worst-case analysis of some aspects of overall disconnection process. Many graph theoretical parameters have been used in the past to describe the stability of communication networks. There are few parameters such as integrity, neighbour-integrity and tenacity number giving the vulnerability. Also, in the neighbour-integrity, if a station is destroyed, the adjacent stations will be betrayed so that the betrayed stations become useless to network as a whole.
In this paper we study the stability of the Extended Fibonacci Cube using the integrity and neighbour-integrity. We compared the obtained results with the results of the other network topologies. We saw that, for two graphs G1 and G2 that have same number of vertices if k(G1) > k(G2), then I(G1) > I(G2) and NI(G1)< NI(G2).