Abstract. A graph is called edge-transitive, if its full automorphism group acts transitively on its edge set. In this paper, we inquire the existence of connected edge-transitive cubic graphs of order 58p 2 for each prime p. It is shown that only for p = 29, there exists a unique edge-transitive cubic graph of order 58p 2 .Key words: Edge-transitive graphs, Symmetric graphs, Semisymmetric graphs, sRegular graphs, Regular coverings.Abstrak. Sebuah graf disebut transitif-sisi jika grup automorfisma penuhnya berlaku secara transitif pada himpunan sisinya. Pada paper ini, kami meneliti keberadaan graf kubik transitif-sisi terhubung berorde 58p 2 untuk setiap bilangan prima p. Kami tunjukkan bahwa hanya untuk p = 29 terdapat graf kubik transitif-sisi unik berorde 58p 2 .

A regular cover of a connected graph is called dihedral ifits transformation group is dihedral. In this paper, the authors clas-sify all dihedral coverings of the Heawood graph whose fibre-preservingautomorphism subgroups act edge-transitively.