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Matrix tree theorems. (English) Zbl 0376.05032

MSC:
05C30 Enumeration in graph theory
05C20 Directed graphs (digraphs), tournaments
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
05A19 Combinatorial identities, bijective combinatorics
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[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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