Counting spanning trees of multiple complete split-like graph containing a given spanning forest

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-10-24 DOI:10.1016/j.disc.2024.114300

引用次数: 0

Abstract

The multiple complete split-like graph

M C S_{b, s}^{a}

is the join of an empty graph

{\overline{K}}_{a}

and s copies of complete graph

K_{b}

. In this article, we obtain the formulas for the number of spanning trees of

M C S_{b, s}^{a}

containing a given spanning forest when

s = 1

and 2. Particularly, when

s = 1

, our result derives the number of spanning trees of complete split graph containing a given spanning forest, thereby extending Moon's result [19].

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对包含给定生成林的多个完整分裂样图的生成树进行计数

多重完整分裂样图 MCSb,sa 是空图 K‾a 和完整图 Kb 的 s 个副本的连接。在本文中，我们得到了当 s=1 和 2 时，MCSb,sa 中包含给定生成林的生成树的数量公式。特别是当 s=1 时，我们的结果推导出了包含给定生成林的完整分裂图的生成树数，从而扩展了 Moon 的结果 [19]。

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 Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.