A certain polynomial of a graph and graphs with an extremal number of trees

  • Kelmans A
  • Chelnokov V
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Abstract

The polynomial we consider here is the characteristic polynomial of a certain (not adjacency) matrix associated with a graph. This polynomial was introduced in connection with the problem of counting spanning trees in graphs [8]. In the present paper the properties of this polynomial are used to construct some classes of graphs with an extremal numbers of spanning trees. © 1974.

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Authors

  • A. K. Kelmans

  • V. M. Chelnokov

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