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arXiv · 2402.07209

Weighted sums of rooted spanning forests on cycles with pendant edges

Hajime Fujita·Kimiko Hasegawa·Yukie Inaba·Takefumi Kondo
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Abstract

We derive two formulas for the weighted sums of rooted spanning forests of particular sequence of graphs by using the matrix tree theorem. We consider cycle graphs with edges so called the pendant edges. One of our formula can be described as a variable transformation of the Chebyshev polynomial. They have particular algebraic properties.

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Hajime Fujita, Kimiko Hasegawa, Yukie Inaba, Takefumi Kondo. 2024-02-11. Weighted sums of rooted spanning forests on cycles with pendant edges. https://arxiv.org/abs/2402.07209

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