A family of edge-transitive Cayley graphs

Alspach, B.: Point-symmetric graphs and digraphs of prime order and transitive permutation groups of prime degree. J. Comb. Theory Ser. B 15, 12–17 (1973)

Alspach, B., Marušič, D., Nowitz, L.: Constructing graphs which are $$1/2$$-transitive. J. Austral. Math. Soc. Ser. A 56(3), 391–402 (1994)

Biggs, N.: Algebraic Graph Theory, 2nd edn. Cambridge University Press, New York (1992)

Bouwer, A.E.: Vertex and edge-transitive but not 1-transitive graphs. Can. Math. Bull. 13, 231–237 (1970)

Cameron, P.J.: Finite permutation groups and finite simple groups. Bull. Lond. Math. Soc. 13, 1–22 (1981)

Chao, C.Y.: On the classification of symmetric graphs with a prime number of vertices. Trans. Am. Math. Soc. 158, 247–256 (1971)

Cheng, Y., Oxley, J.: On weakly symmetric graphs of order twice a prime. J. Comb. Theory Ser. B 42, 196–211 (1987)

Conder, M.D.E., Marušič, D.: A tetravalent half-arc-transitive graph with non-abelian vertex stabilizer. J. Comb. Theory Ser. B 88, 67–76 (2003)

Ding, S.Y., Ling, B., Lou, B.G., Pan, J.M.: Pentavalent symmetric graphs of square-free order. Graphs Comb. 32, 2355–2366 (2016)

Dixon, J., Mortimer, B.: Permutation Groups. Springer, New York (1996)

Feng, Y.-Q., Kwak, J.H.: Constructing an infinite family of cubic 1-regular graphs. European J. Combin. 23(5), 559–565 (2002)

Frucht, R.: A one-regular graph of degree three. Can. J. Math. 4, 240–247 (1952)

Godsil, C.D.: On the full automorphism group of a graph. Combinatorica 1, 243–256 (1981)

Hammack, R., Imrich, W., Klavžar, S.: Edge-transitive products. J. Algebraic Combin. 43(4), 837–850 (2016)

Li, C.H.: On isomorphisms of connected Cayley graphs. Discrete Math. 178, 109–122 (1998)

Li, C.H., Pan, J.M., Song, S.J., Wang, D.J.: A characterization of a family of edge-transitive metacirculant graphs. J. Comb. Theory Ser. B 107, 12–25 (2014)

Li, C.H., Lu, Z.P., Wang, G.X.: The vertex-transitive and edge-transitive tetravalent graphs of square-free order. J. Algebraic Combin. 42(1), 25–50 (2015)

Li, C.H., Lu, Z.P., Wang, G.X.: On edge-transitive graphs of square-free order. Electr. J. Comb. 22(3), 3–25 (2015)

Li, C.H., Lu, Z.P., Wang, G.X.: Arc-transitive graphs of square-free order and small valency. Discrete Math. 339, 2907–2918 (2016)

Liu, G.X., Lu, Z.P.: On edge-transitive cubic graphs of square-free order. European J. Combin. 45, 41–46 (2015)

Marušič, D.: A family of one-regular graphs of valency 4. European J. Combin. 18(1), 59–64 (1997)

Marušič, D.: Recent developments in half-transitive graps. Discrete Math. 182, 219–231 (1998)

Marušič, D., Šparl, P.: One-regular graphs and half-transitive graphs of valency 4. European J. Combin. 19, 345–354 (1998)

Marušič, D.: On 2-arc-transitivity of Cayley graphs. J. Comb. Theory Ser. B 87, 162–196 (2003)

Pan, J.M.: Locally primitive Cayley graphs of dihedral groups. European J. Combin. 36, 39–52 (2014)

Praeger, C.E., Xu, M.Y.: Vertex-primitive graphs of order a product of two distinct primes. J. Comb. Theory Ser. B 59, 245–266 (1993)

Praeger, C.E., Wang, R.J., Xu, M.Y.: Symmetric graphs of order a product of two distinct primes. J. Comb. Theory Ser. B 58, 299–318 (1993)

Suzuki, M.: Group Theroy II. Springer, New York (1985)

Wang, R.J., Xu, M.Y.: A classification of symmetric graphs of order $$3p$$. J. Comb. Theory Ser. B 58, 197–216 (1993)

Tutte, W.T.: Connectivity in Graphs. University of Toronto Press, Toronto (1966)