Abstract
It is important that a communication service has to service dependability by high level. Many affairs cause failures in a network. Destroying nodes or links in communication network, cable cuts, node interruptions, software errors or hardware failures and transmission failure at various points, human error or accident and can interrupt service for long periods of time. At the beginning a communication network, requiring greater degree of stability or less vulnerability. In this work, various stability measures of a communication network are defined and the stability measures of some static interconnection networks which are known long times and w-star networks that are a new graph class, are given.