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链图的距离特征值

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如果一个图G不包含2K2,C3及C5作为导出子图,称其为链图.在所有点数和边数给定的连通二部图中,链图具有最大的谱半径,这使得链图在图谱理论中占有一席之地.本文研究了连通链图距离特征值的分布情况.对于点数为n的连通链图G=G(t1,…,th;s1,…,sh),我们证明了-2是G的重数为n-2h的距离特征值,且G有h-1个距离特征值小于-2和h+1个距离特征值大于-2.
The distance spectra of chain graphs
A graph is called a chain graph if it does not contain induced 2K2,C3 or C5.In spectral graph theory,chain graphs feature as graphs whose largest eigenvalue within the connected bipartite graphs of fixed order and size is maximal.In this paper,we consider the distance eigenvalues of a connected chain graph G.We present that-2 is an eigenvalue of G=G(t1,…,th;s1,…,sh),with multiplicity n-2h.And further more,there are exactly h-1 eigenvalues less than-2 and exactly h+1 eigenvalues greater than-2.

chain graphsdistance spectrumequitable partition

吕雪征、马梦郁

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中国人民大学数学学院,北京 100872

链图 距离特征值 合理划分

国家自然科学基金

11971479

2024

运筹学学报
中国运筹学会

运筹学学报

CSTPCD北大核心
影响因子:0.25
ISSN:1007-6093
年,卷(期):2024.28(1)
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