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ENUMERATION OF HAMILTONIAN CYCLES AND PATHS IN A GRAPH

By C. J. Liu and Communicated Andrew Odlyzko

Abstract

Abstract. First, we show that the determinant of a given matrix can be expanded by its principal minors together with a set of arbitrary parameters. The enumeration of Hamiltonian cycles and paths in a graph is then carried out by an algebraic method. Three types of nonalgebraic representation are formulated. The first type is given in terms of the determinant and permanent of a parametrized adjacent matrix. The second type is presented by a determinantal function of multivariables, each variable having domain {0, 1}. Formulas of the third type are expressed by spanning trees of subgraphs. When applying the formulas to a complete multipartite graph, one can easily find the results

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.360.2564
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