Article history: Received 14 November 2008 Received in revised form 15 January 2012 Accepted 27 February 2012 Available online xxxx

In the eternal dominating set problem, guards form a dominating set on a graph and at each step, a vertex is attacked. After each attack, if the guards can “move” to form a dominating set that contains the attacked vertex, then the guards have successfully defended against the attack. We wish to determine the minimum number of guards required to successfully defend against any possible sequence...

In this paper, we define fuzzy graph chains, which comprise vertex identification. These graphs are isomorphic graphs, provide that after applying various features to the chain of as special .