PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 39(53), pp. 6367 (1986) 

AN APPLICATION OF CIRCUIT POLYNOMIALS TO THE COUNTING OF SPANNING TREES IN GRAPHSE. J. Farrell and J. C. GrellDepartment of Mathematics, The University of the West Indies, St. Augustine, TrinidadAbstract: $t$ is shown that the number of spanning trees in a graph can be obtained from the circuit polynomial of an associated graph. From this, the number of spanning tress in a regular graph is shown to be obtainable from the characteristic polynomial of a nodedeleted subgraph. Finally, Cayley's theorem for the number of labelled tress is derived. Classification (MSC2000): 05C99 Full text of the article:
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