When the nodes or links of communication networks are destroyed,
its effectiveness decreases. Thus, we must design the communication network as stable as possible, not only with respect to the initial disruption, but also with respect to the possible reconstruction of the network. A graph is considered as a modeling network, many graph theoretic parameters have been ušed to describe the stability of communication networks, including connectivity, integrity, tenacity. Several of these deal with two fundamental questions about the resulting graph. How many vertices can still communicate? How difficult is it to reconnect the graph? Stability numbers of a graph measure its durability respect to break down. The neighbour-integrity of a graph is a measure of graph vulnerability. In the neighbour-integrity, it is considered that any failure vertex effects its neighbour vertices. In this work, we define the accessible sets and accessibility number and we consider the neighbour-integrity of Generalised Petersen graphs and the relation with its accessibility number.
The vulnerability of the communication network measures the resistance of the network to disruption of operation after the failure of certain stations or communication links. Cable cuts, node interruptions, software errors or hardware failures and transmission failure at various points can cause interrupt service for long periods of time. High levels of service dependability have traditionally characterised communication services. In communication networks, requiring greater degrees of stability or less vulnerability. If we think of graph G as modelling a network, the neighbour-integrity and edge-neighbour-integrity of a graph, which are considered as the neighbour vulnerability, are two measures of graph vulnerability. In the neighbour-integrity, it is considered that any failure vertex affects its neighbour vertices. In the edge-neighbour-integrity it is consider that any failure edge affects its neighbour edges.
In this paper we study classes of recursive graphs that are used to design communication networks and represent the molecular structure, and we show neighbour-integrity (vertex and edge) among the recursive graphs.
When a network begins losing nodes or links there is, eventually, a loss in its effectiveness. Thus, a communication network must be constructed to be as stable as possible, not only with respect to tlie initial disruption, but also with respect to the possible reconstruction of the network. When any disruption happens in a cornmunication network two questions are considered: How many vertices can still communicate? How difficult is it to reconnect the network? If a graph is considered as a modeling network, then the above questions can be answered by the graphs. Many graph parameters have been used to deseribe the stability of communication networks, including connectivity, integrity, and tougliness and the binding number. The thorny graphs are special classes of graphs that represent some static interconnection networks. In tliis work, we have given the tenacity of thorny graphs of static interconnection networks.