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Symmetry of graphs has been extensively studied over the past fifty years by using automorphisms of graphs and group theory which have played and still play an important role for graph theory, and promising and interesting results have been obtained, see for examples, [L.W. Beineke, R.doi:10.1016/j.disc.2009.02.027 fatcat:e5d2g7vyq5aahg4jqfzrmojfwe