{"title":"The sum of squares of degrees of bipartite graphs","authors":"M. G. Neubauer","doi":"10.1007/s10474-023-01379-7","DOIUrl":null,"url":null,"abstract":"<div><p>Let <i>G</i> be a subgraph of the complete bipartite graph <span>\\(K_{l,m},{l \\leq m}\\)</span>, with <span>\\(e=qm+p>0\\)</span>, <span>\\(0 \\leq p <m\\)</span>, edges. The maximal value of the sum of the squares of the degrees of the vertices of <i>G</i> is <span>\\(qm^2+p^2+ p (q+1)^2+(m-p) q^2\\)</span>. We classify all graphs that attain this bound using the diagonal sequence of a partition. </p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"171 1","pages":"1 - 11"},"PeriodicalIF":0.6000,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10474-023-01379-7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let G be a subgraph of the complete bipartite graph \(K_{l,m},{l \leq m}\), with \(e=qm+p>0\), \(0 \leq p <m\), edges. The maximal value of the sum of the squares of the degrees of the vertices of G is \(qm^2+p^2+ p (q+1)^2+(m-p) q^2\). We classify all graphs that attain this bound using the diagonal sequence of a partition.
期刊介绍：
Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
