Express the number of spanning trees in term of degrees
作者：
Highlights：
• Page 2, the first line below Theorem 1: The set NSTu(T) is revised to the set of non-spanning trees T such that u∈V(T) and G−V(T) has no isolated vertices.
• Add two lemmas in the beginning of Section 3. The purpose is to apply them to simplify the proof of Theorem 3.
• The proof of Theorem 3 has been revised according to the suggestion from one of the reviewers to consider the set of spanning digraphs D which have the property that idD(vn)=0 and idD(vi)=1 for each i∈[n−1].
• In page 8, we add a paragraph for an upper bound of τ(G) and a corollary.
摘要
•Page 2, the first line below Theorem 1: The set NSTu(T) is revised to the set of non-spanning trees T such that u∈V(T) and G−V(T) has no isolated vertices.•Add two lemmas in the beginning of Section 3. The purpose is to apply them to simplify the proof of Theorem 3.•The proof of Theorem 3 has been revised according to the suggestion from one of the reviewers to consider the set of spanning digraphs D which have the property that idD(vn)=0 and idD(vi)=1 for each i∈[n−1].•In page 8, we add a paragraph for an upper bound of τ(G) and a corollary.
论文关键词：Spanning tree,Degree,Graph polynomial
论文评审过程：Received 15 June 2021, Revised 20 September 2021, Accepted 25 September 2021, Available online 10 October 2021, Version of Record 10 October 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126697
