電路秩 是從一個具有 條圖邊和 個節點的無向圖中,必須移除的最少圖邊數,使得圖中不再有圖環。電路秩也給出了圖的環基中的基本環的數量 (Harary 1994, pp. 37-40; White 2001, p. 56)。這個概念最初由古斯塔夫·基爾霍夫 (Gustav Kirchhoff) 提出 (Kirchhoff 1847; Veblen 1916, p. 9; Kotiuga 2010, p. 20),並且已經被許多不同的名稱和符號引用,如下表所示。
名稱
參考文獻
電路秩
環秩
Harary (1994, p. 39), White (2001, p. 56), Gross and Yellen (2006, pp. 192 and 661)
(第一)圖貝蒂數
White (2001), Gross and Yellen (2006, pp. 192)
圈數
Listing (1862), Veblen (1916, pp. 9 and 18)
圖的零度
符號
參考文獻
Veblen (1916, pp. 9 and 18), Volkmann (1996), Babić et al. (2002)
Gross and Yellen (2006, pp. 192 and 661), White (2001, p. 56)
Ahrens, W. "Über das Gleichungssystem einer Kirchhoffschen galvanischen Stromverzweigung." Math. Ann.49, 311-324, 1897.Babić, D.; Klein, D. J.; Lukovits, I.; Nikolić, S.; and Trinajstić, N. "Resistance-Distance Matrix: A Computational Algorithm and Its Applications." Int. J. Quant. Chem.90, 166-176, 2002.Devillers, J. and Balaban, A. T. (Eds.). Topological Indices and Related Descriptors in QSAR and QSPR. Amsterdam, Netherlands: Gordon and Breach, 1999.Gross, J. T. and Yellen, J. Graph Theory and Its Applications, 2nd ed. Boca Raton, FL: CRC Press, 2006.HararyHarary, F. Graph Theory. Reading, MA: Addison-Wesley, 1994.Kirchhoff, G. "Über die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Verteilung galvanischer Ströme geführt wird." Ann. d. Phys. Chem.72, 497-508, 1847.König, D. Theorie der endlichen und unendlichen Graphen. Leipzig, Germany: Akademische Verlagsgesellschaft, 1936.Kotiuga, P. R. A Celebration of the Mathematical Legacy of Raoul Bott. Providence, RI: Amer. Math. Soc., 2010.Listing, J. B. Census raumliche Komplexe. Göttingen, Germany: 1862.Mateti, P. and Deo, N. "On Algorithms for Enumerating All Circuits of a Graph." SIAM J. Comput.5, 90-99, 1976.Veblen, O. Analysis Situs. New York: Amer. Math. Soc., 1916.Volkmann, L. "Estimations for the Number of Cycles in a Graph." Per. Math. Hungar.33, 153-161, 1996.White, A. T. "Imbedding Problems in Graph Theory." Ch. 6 in Graphs of Groups on Surfaces: Interactions and Models (Ed. A. T. White). Amsterdam, Netherlands: Elsevier, pp. 49-72, 2001.Wilson, R. J. Introduction to Graph Theory. Edinburgh: Oliver and Boyd, p. 46, 1971.