Behzad, M. and Chartrand, G. "No Graph is Perfect." Amer. Math. Monthly74, 962-963, 1967.Eggleton, R. B. "Graphic Sequences and Graphic Polynomials." In Infinite and Finite Sets (Ed. A. Hajnal). Amsterdam, Netherlands: North-Holland, pp. 385-293, 1975.Erdős, P. and Gallai, T. "Graphs with Prescribed Degrees of Vertices" [Hungarian]. Mat. Lapok.11, 264-274, 1960.Fulkerson, D. R. "Upsets in Round Robin Tournaments." Canad. J. Math.17, 957-969, 1965.Fulkerson, D. R.; Hoffman, A. J.; and McAndrew, M. H. "Some Properties of Graphs with Multiple Edges." Canad. J. Math.17, 166-177, 1965.Hakimi, S. "On the Realizability of a Set of Integers as Degrees of the Vertices of a Graph." SIAM J. Appl. Math.10, 496-506, 1962.Havel, V. "A Remark on the Existence of Finite Graphs" [Czech]. Časopis Pest. Mat.80, 477-480, 1955.Ryser, H. J. "Combinatorial Properties of Matrices of Zeros and Ones." Canad. J. Math.9, 371-377, 1957.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, p. 157, 1990.Tripathi, A. and Vijay, S. "A Note on a Theorem of Erdős & Gallai." Discr. Math.265, 417-420, 2003.
是图形的当且仅当顶点度的总和为偶数且序列服从以下性质
(Skiena 1990, p. 157)，并且此条件也推广到有向图。 Tripathi 和 Vijay (2003) 表明，此不等式只需要检查序列中不同项的数量，而不需要检查所有 
，而不是所有 
。
和 
的度序列是图形的当且仅当序列 
是图形的。此外，Havel (1955) 和 Hakimi (1962) 表明，如果度序列是图形的，则存在一个图 
，使得最高度数的节点与
个次最高度数顶点相邻，其中 
，其中 
是 
的最大顶点度。