The sum of squares of degrees of bipartite graphs

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2023-10-31 DOI:10.1007/s10474-023-01379-7

M. G. Neubauer

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.

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二部图的度数平方和

设G是完全二部图\(K_{l,m},{l \leq m}\)的一个子图，它有\(e=qm+p>0\), \(0 \leq p <m\)条边。G的顶点度数平方和的最大值是\(qm^2+p^2+ p (q+1)^2+(m-p) q^2\)。我们用划分的对角序列对所有达到这个界的图进行分类。

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

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

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.