{"title":"Counting spanning trees of multiple complete split-like graph containing a given spanning forest","authors":"Chenlin Yang, Tao Tian","doi":"10.1016/j.disc.2024.114300","DOIUrl":null,"url":null,"abstract":"<div><div>The multiple complete split-like graph <span><math><mi>M</mi><mi>C</mi><msubsup><mrow><mi>S</mi></mrow><mrow><mi>b</mi><mo>,</mo><mi>s</mi></mrow><mrow><mi>a</mi></mrow></msubsup></math></span> is the join of an empty graph <span><math><msub><mrow><mover><mrow><mi>K</mi></mrow><mo>‾</mo></mover></mrow><mrow><mi>a</mi></mrow></msub></math></span> and <em>s</em> copies of complete graph <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>b</mi></mrow></msub></math></span>. In this article, we obtain the formulas for the number of spanning trees of <span><math><mi>M</mi><mi>C</mi><msubsup><mrow><mi>S</mi></mrow><mrow><mi>b</mi><mo>,</mo><mi>s</mi></mrow><mrow><mi>a</mi></mrow></msubsup></math></span> containing a given spanning forest when <span><math><mi>s</mi><mo>=</mo><mn>1</mn></math></span> and 2. Particularly, when <span><math><mi>s</mi><mo>=</mo><mn>1</mn></math></span>, our result derives the number of spanning trees of complete split graph containing a given spanning forest, thereby extending Moon's result <span><span>[19]</span></span>.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 2","pages":"Article 114300"},"PeriodicalIF":0.7000,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X2400431X","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The multiple complete split-like graph is the join of an empty graph and s copies of complete graph . In this article, we obtain the formulas for the number of spanning trees of containing a given spanning forest when and 2. Particularly, when , our result derives the number of spanning trees of complete split graph containing a given spanning forest, thereby extending Moon's result [19].
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.