### 博碩士論文 107221004 詳細資訊

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(Counting Trees: A Review of Methods)

 ★ 圓環面網路上的病毒散播 ★ 以2D HP 模型對蛋白質摺疊問題之研究 ★ On Steiner centers of graphs ★ On the Steiner medians of a block graph ★ 圖形列表著色 ★ 秩為5的圖形 ★ Some results on distance-two labeling of a graph ★ 關於非奇異線圖的樹 ★ On Minimum Strictly Fundamental Cycle Basis ★ 目標集選擇問題 ★ 路徑圖與格子圖上的目標集問題 ★ 超立方體圖與格子圖上的目標集問題 ★ 圖形環著色數的若干等價定義 ★ 網格圖上有效電阻計算方法的比較 ★ d 維立方體圖上有效電阻與首達時間的計算方法

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vertices, how many spanning trees does G contain? In this article, we summarized and reviewed the existing methods and theorems in the published literature that answer this question. We try to give the proofs of the results in a more explanatory and graphic way.

★ 生成樹

2 Counting Spanning Forests 2
3 Counting Rooted Directed Trees 4
4 Matrix Tree Theorem via Deletion Contraction Recurrence 7
5 Cayley′s Formula via Prüfer Code 10
6 Cayley′s Formula via Joyal′s Combinatorial Argument 12
7 Counting Weighted Rooted Directed Trees 14
References 17

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[11] Hong-Gwa Yeh, Class Notes for Graph Theory, Spring 2020, National Central University, Taiwan.