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Matrix tree theorems. (English) Zbl 0376.05032

05C30 Enumeration in graph theory
05C20 Directed graphs (digraphs), tournaments
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
05A19 Combinatorial identities, bijective combinatorics
Full Text: DOI
[1] Cayley, A, A theorem on trees, Quart. J. math. Oxford ser., 23, 376-378, (1889) · JFM 21.0687.01
[2] Kirchhoff, G; Kirchhoff, G, Über die auflösung der gleichungen, auf welche man bei der untersuchung der linearen verteilung galvanischer ströme gefuhrt wird, Ann. phys. chem., IRE trans. circuit theory, 72, 4-7, (1958), CT-5
[3] Maxwell, J.C, A treatise on electricity and magnetism I, (), 403-410, (Reprinted by Dover Publications)
[4] Moon, J.W, Various proofs of Cayley’s formula for counting trees, (), 70-78
[5] Moon, J.W, Counting labelled trees, (), 39-48, Chap. 5 · Zbl 0214.23204
[6] Rényi, A, On the enumeration of trees, (), 355-360
[7] Trent, H.M, Note on the enumeration and listing of all possible trees in a connected linear graph, (), 1004-1007 · Zbl 0055.42204
[8] Tutte, W.T, The dissection of equilateral triangles into equilateral triangles, (), 463-482 · Zbl 0030.40903
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