Generating formulas for the number of trees in a graph. (English) Zbl 0135.41904


Full Text: DOI


[1] Cayley, A., (), 26-28
[2] Riordan, J., An introduction to combinatorial analysis, (1958), John Wiley and Sons, Inc., New York, Chapt. 6 · Zbl 0078.00805
[3] Weinberg, L., Number of trees in a graph, (), 1954-1955, No. 12
[4] Bedrosian, S.D., Formulas for the number of trees in a network, IRE trans. on circuit theory, Vol. CT-8, 363-364, (1961)
[5] Bedrosian, S.D., Application of linear graphs to multilevel maser analysis, Jour. Frank. inst., Vol. 274, No. 4, 278-283, (1962)
[6] Bedrosian, S.D., Properties of linear graphs based on trees, () · Zbl 0297.05125
[7] O’Neil, P.V., The number of trees in a certain network, () · Zbl 0229.05121
[8] Ore, O., Theory of graphs, () · JFM 68.0039.01
[9] Mayeda, W., Reducing computation time in the analysis of networks by digital computer, IRE trans. on circuit theory, Vol. CT-6, No. 1, (1959)
[10] Weinberg, L., Network analysis and synthesis, (), 165
[11] Bedrosian, S.D., Evaluation of network determinants via the key subgraph, (), to appear in Conf. Proc. · Zbl 0298.05104
[12] Kirchhoff, G.; Kirchhoff, G., Über die auflösung der gleichungen, auf welche man bei der untersuchungen der linearen verteilung galvanisher ströme geführt wird, Poggendorf ann. physik, Trans. inst. radio engrs., CT-5, 4-7, (1958), English translation
[13] Wang, K.T., On a new method for the analysis of networks, (), 1-11, Memoir No. 2
[14] Otter, R., The number of trees, Ann. math., Vol. 49, 583-599, (1948) · Zbl 0032.12601
[15] Ku, Y.H., Résumé of Maxwell’s and Kirchhoff’s rules, Jour. Frank. inst., Vol. 253, No. 3, 211-224, (1952)
[16] Percival, W.S., Solution of passive electrical networks by means of mathematical trees, Jour. inst. elect. engrs. (London), Vol. 100, Part III, 143-150, (1953)
[17] Trent, H.M., Note on the enumeration and listing of all possible trees in a connected linear graph, (), 1004-1007 · Zbl 0055.42204
[18] Nakagawa, N., On the evaluation of graph trees and driving point admittance, Trans. inst. radio engrs., CT-5, 122-127, (1958)
[19] Kim, W.H.; Younger, D.H.; Freiman, C.V.; Mayeda, W., On iterative factorization in network analysis by digital computers, ()
[20] Hakimi, S.L., On trees of a graph and their generation, Jour. Frank. inst., Vol. 272, No. 5, 347-359, (1961) · Zbl 0137.43003
[21] Hirayama, H.; Wantanabe, H.; Harada, K., Digital determination of trees in network topology, Jour. inst. elec. comm. engrs. (Japan), Vol. 46, No. 1, 23-30, (1963)
[22] Lee, S.C., On topological formulae, (), to appear in Conf. Proc.
[23] Seshu, S.; Reed, M.B., Linear graphs and electrical networks, (1961), Addison-Wesley Publishing Co., Inc., Reading, Mass · Zbl 0102.34001
[24] Berge, C., The theory of graphs and its applications, (1962), Methuen and Co., London, English Translation · Zbl 0097.38903
[25] Kim, W.H.; Chien, R.T., Topological analysis and synthesis of communication networks, (1962), Columbia University Press New York · Zbl 0119.22302
[26] Stewart, F.M., Introduction to linear algebra, (1963), D. Van Nostrand Company, Inc., Princeton, N. J · Zbl 0111.01306
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.