Babai, L. Problem 17 in "Unsolved Problems." In Summer Research Workshop in Algebraic Combinatorics. Simon Fraser University, Jul. 1979.Babai, L. "Automorphism Groups, Isomorphism, Reconstruction." Ch. 27 in Handbook of Combinatorics, Vol. 2 (Ed. R. L. Graham, M. Grötschel, M.; and L. Lovász). Cambridge, MA: MIT Press, pp. 1447-1540, 1996.Bermond, J.-C. "Hamiltonian Graphs." Ch. 6 in Selected Topics in Graph Theory (Ed. L. W. Beineke and R. J. Wilson). London: Academic Press, pp. 127-167, 1979.Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, 1976.Bryant, D. and Dean, M. "Vertex-Transitive Graphs that have no Hamilton Decomposition." 25 Aug 2014. http://arxiv.org/abs/1408.5211.Godsil, C. and Royle, G. "Hamilton Paths and Cycles." C§3.6 in Algebraic Graph Theory. New York: Springer-Verlag, pp. 45-47, 2001.Gould, R. J. "Updating the Hamiltonian Problem--A Survey." J. Graph Th.15, 121-157, 1991.Kutnar, K. and Marušič, D. "Hamilton Cycles and Paths in Vertex-Transitive Graphs-Current Directions." Disc. Math.309, 5491-5500, 2009.Lipman, M. "Hamiltonian Cycles and Paths in Vertex-Transitive Graphs with Abelian and Nilpotent Groups." Disc. Math.54, 15-21, 1985.Marušič, D. "Hamiltonian Paths in Vertex-Symmetric Graphs of Order ." Disc. Math.42, 227-242, 1982.Marušič, D. and Parsons, T. D. "Hamiltonian Paths in Vertex-Symmetric Graphs of Order ." Disc. Math.43, 91-96, 1983.Mütze, T. "Proof of the Middle Levels Conjecture." Proc. Lond. Math. Soc.112, 677-713, 2016.Mütze, T. "On Hamilton Cycles in Graphs Defined by Intersecting Set Systems." Not. Amer. Soc.74, 583-592, 2024.Royle, G. "Transitive Graphs." http://school.maths.uwa.edu.au/~gordon/trans/.Thomassen, C. "Tilings of the Torus and the Klein Bottle and Vertex-Transitive Graphs on a Fixed Surface." Trans. Amer. Math. Soc.323 605-635, 1991.
、彼得森图 
、考克斯特图 
、三角形替换 彼得森图 和 三角形替换 考克斯特图。正如 Gould (1991) 引用 Bermond (1979) 所述，Thomassen 推测所有其他 连通 顶点传递图 都是 哈密顿图（参见 Godsil 和 Royle 2001，第 45 页；Mütze 2024）。相比之下，Babai (1979, 1996) 推测存在无限多个连通的非哈密顿顶点传递图。
的每个连通 顶点传递图 (除了 彼得森图) 都是 哈密顿图。Marušič (1982) 证明了阶数为 
、
、
和 
的每个连通顶点传递图都是 哈密顿图，而 Marušič 和 Parsons (1983) 表明阶数为 
和 
的连通顶点传递图是 可追踪的 (Gould 1991)。
." Disc. Math. 42, 227-242, 1982.Marušič, D. and Parsons, T. D. "Hamiltonian Paths in Vertex-Symmetric Graphs of Order 
." Disc. Math. 43, 91-96, 1983.Mütze, T. "Proof of the Middle Levels Conjecture." Proc. Lond. Math. Soc. 112, 677-713, 2016.Mütze, T. "On Hamilton Cycles in Graphs Defined by Intersecting Set Systems." Not. Amer. Soc. 74, 583-592, 2024.Royle, G. "Transitive Graphs."