Weighted Moon-type formulae for complete graphs and complete bipartite graphs

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-04-30 DOI:10.1016/j.dam.2025.04.058

Jun Ge

引用次数: 0

Abstract

In 1964, Cayley’s formula was generalized to a fascinating formula on the number of spanning trees of

K_{n}

containing a given spanning forest by J.W. Moon. It was not until 58 years later that the second Moon-type formula was discovered for

K_{m, n}

by Dong and the author. In this note, we obtain weighted versions for these two Moon-type formulae with much shorter proofs.

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完全图和完全二部图的加权moon型公式

1964年，J.W. Moon将Cayley公式推广为包含给定生成林的Kn的生成树数目的一个令人着迷的公式。直到58年后，董教授和作者才发现了Km，n的第二个月球型公式。在本文中，我们用更短的证明得到了这两个月型公式的加权版本。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.