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Chordal 2-Connected Graphs and Spanning Trees

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Abstract

We present a transformation on a chordal 2-connected simple graph that decreases the number of spanning trees. Based on this transformation, we show that for positive integers n, m with math formula, the threshold graph math formula having n vertices and m edges that consists of an math formula-clique and math formula vertices of degree 2 is the only graph with the fewest spanning trees among all 2-connected chordal graphs on n vertices and m edges.

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