Weighted sums of rooted spanning forests on cycles with pendant edges

Hajime Fujita; Kimiko Hasegawa; Yukie Inaba; Takefumi Kondo

Weighted sums of rooted spanning forests on cycles with pendant edges

Combinatorics 2024-02-13 v1 Rings and Algebras

Authors: Hajime Fujita , Kimiko Hasegawa , Yukie Inaba , Takefumi Kondo

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.

Keywords

weighted sums rooted spanning forests cycle graphs pendant edges matrix tree theorem Chebyshev polynomial

Cite

@article{arxiv.2402.07209,
  title  = {Weighted sums of rooted spanning forests on cycles with pendant edges},
  author = {Hajime Fujita and Kimiko Hasegawa and Yukie Inaba and Takefumi Kondo},
  journal= {arXiv preprint arXiv:2402.07209},
  year   = {2024}
}

Comments

10 pages, 7 figures

Weighted sums of rooted spanning forests on cycles with pendant edges

Abstract

Keywords

Cite

Comments

Related papers