一個圖是平面的當且僅當它有一個組合對偶圖 (Harary 1994, p. 115)。任何平面圖都有一個圖嵌入，即平面直線嵌入，其中邊不相交 (Fáry 1948; Bryant 1989; Skiena 1990, pp. 100 and 251; Scheinerman and Wilf 1994)。
Auslander, L. and Parter, S. "On Imbedding Graphs in the Sphere." J. Math. Mechanics10, 517-523, 1961.Battle, J.; Harary, F.; and Kodama, Y. "Every Planar Graph with Nine Points has a Nonplanar Complement." Bull. Amer. Math. Soc.68, 569-571, 1962.Booth, K. S. and Lueker, G. S. "Testing for the Consecutive Ones Property, Interval Graphs, and Graph Planarity using PQ-Tree Algorithms." J. Comput. System Sci.13, 335-379, 1976.Bryant, V. W. "Straight Line Representation of Planar Graphs." Elem. Math.44, 64-66, 1989.Cai, J.; Han, X.; and Tarjan, R. "New Solutions to Four Planar Graph Problems." Technical Report. New York University, 1990.Di Battista, G.; Eades, P.; Tamassia, R.; and Tollis, I. G. Graph Drawing: Algorithms for the Visualization of Graphs. Englewood Cliffs, NJ: Prentice-Hall, 1998.Eades, P. and Tamassia, R. "Algorithms for Drawing Graphs: An Annotated Bibliography." Technical Report CS-89-09. Department of Computer Science. Providence, RI: Brown University, Feb. 1989.Eppstein, D. "Layered Graph Drawing." http://www.ics.uci.edu/~eppstein/junkyard/thickness/.Even, S. Graph Algorithms. Rockville, MD: Computer Science Press, 1979.Fáry, I. "On Straight Line Representations of Planar Graphs." Acta Sci. Math. (Szeged(11, 229-233, 1948.Gardner, M. The Sixth Book of Mathematical Games from Scientific American. Chicago, IL: University of Chicago Press, pp. 91-94, 1984.Harary, F. "Planarity." Ch. 11 in Graph Theory. Reading, MA: Addison-Wesley, pp. 102-125, 1994.Harborth, H. and Möller, M. "Minimum Integral Drawings of the Platonic Graphs." Math. Mag.67, 355-358, 1994.Hopcroft, J. and Tarjan, R. "Efficiency Planarity Testing." J. ACM21, 549-568, 1974.Karpov, D. V. "Upper Bound on the Number of Edges of an Almost Planar Bipartite Graph." 3 Jul 2013. https://arxiv.org/abs/1307.1013.Kocay, W. and Pantel, C. "An Algorithm for Finding a Planar Layout of a Graph with a Regular Polygon as Outer Face." Util. Math.48, 161-178, 1995.Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 56, 1983.Nishizeki, T. and Rahman, M. S. Planar Graph Drawing. Singapore: World Scientific, 2004.Read, R. C. "A New Method for Drawing a Planar Graph Given the Cyclic Order of the Edges at Each Vertex." Congr. Numer.56, 31-44, 1987.Scheinerman, E. and Wilf, H. S. "The Rectilinear Crossing Number of a Complete Graph and Sylvester's 'Four Point' Problem of Geometric Probability." Amer. Math. Monthly101, 939-943, 1994.Skiena, S. "Planar Graphs." §6.5 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 247-253, 1990.Sloane, N. J. A. Sequences A003094/M1652, A005470/M1252, A049370, A049371, A049372, and A049373 in "The On-Line Encyclopedia of Integer Sequences."Steinbach, P. Field Guide to Simple Graphs. Albuquerque, NM: Design Lab, 1990.Stony Brook Algorithm Repository. §1.4.12. "Planarity Detection and Embedding." http://www.cs.sunysb.edu/~algorith/files/planar-drawing.shtml.Wagon, S. "Coloring Planar Maps and Graphs." Ch. 24 in Mathematica in Action, 2nd ed. New York: Springer-Verlag, pp. 507-537, 1999.West, D. B. Introduction to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, p. 243, 2000.Whitney, H. "Non-Separable and Planar Graphs." Trans. Amer. Math. Soc.34, 339-362, 1932.Whitney, H. "Planar Graphs." Fund. Math.21, 73-84, 1933.Wilson, R. J. Introduction to Graph Theory. London: Longman, 1975.
, 2, ... 個節點的平面圖的數量分別為 1, 2, 4, 11, 33, 142, 822, 6966, 79853, ... (OEIS A005470; Wilson 1975, p. 162)，其中前幾個如圖所示。
演算法 (1961; Skiena 1990, p. 247)。可以使用 Wolfram 語言 中的命令測試圖的平面性：PlanarGraphQ[g].
是平面的，那麼 
至少有一個頂點度 
。如果圖 
及其圖的補圖 
都是平面的，那麼 
最多有八個頂點。
時是平面的。完全二部圖 
是非平面的。更一般地，Kuratowski 在 1930 年證明，一個圖是平面的當且僅當它不包含任何完全圖 
或 
的圖擴充套件。
的平面圖的數量。
, 2, 3, ...