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On Family of Graphs with Minimum Number of Spanning Trees

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Abstract

We show that there is a well-defined family of connected simple graphs Λ(n, m) on n vertices and m edges such that all graphs in Λ(n, m) have the same number of spanning trees, and if \({G \in \Lambda(n, m)}\) then the number of spanning trees in G is strictly less than the number of spanning trees in any other connected simple graph \({H, H \notin \Lambda(n, m)}\) , on n vertices and m edges.

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  1. Armament Research, Development and Engineering Center, Picatinny, NJ, 07806, USA

    Zbigniew R. Bogdanowicz

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  1. Zbigniew R. Bogdanowicz
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Correspondence to Zbigniew R. Bogdanowicz.

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Bogdanowicz, Z.R. On Family of Graphs with Minimum Number of Spanning Trees. Graphs and Combinatorics 29, 1647–1652 (2013). https://doi.org/10.1007/s00373-012-1228-1

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  • DOI: https://doi.org/10.1007/s00373-012-1228-1

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