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  • A graph is called edge-transitive, if its full automorphismgroup acts transitively on its edge set. In this paper, we inquire theexistence of connected edge-transitive cubic graphs of order 58p2foreach prime p. It is shown that only for p = 29, there exists a uniqueedge-transitive cubic graph of order 58p2.DOI : http://dx.doi.org/10.22342/jims.21.2.193.117-126