A certain polynomial of a graph and graphs with an extremal number of trees |
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Authors: | AK Kelmans VM Chelnokov |
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Institution: | Institute of Control Sciences, Moscow, USSR |
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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. |
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