ENUMERATION OF SPANNING-TREES OF CERTAIN GRAPHS

RUSSIAN MATHEMATICAL SURVEYS（1990）

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摘要

In this paper, we dene and study polynomials that enumerate spanning trees according to degrees of all vertices. These polynomials have a certain reciprocity. A formula that reduces the polynomials for multipartite graphs to the polynomials for component graphs is also found. There is a generalization of Prufer's coding that corresponds to the latter formula. All results are extended to the case of oriented nets.

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关键词

matrix-tree theorem.,pr ufer's coding,multipartite graph,oriented net,. spanning tree,reciprocity

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