Some spectral properties and characterizations of connected odd-bipartite uniform hypergraphs
Some spectral properties and characterizations of connected odd-bipartite uniform hypergraphs
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DOI：
10.1080/03081087.2015.1009061
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发表时间：
2014-03
影响因子：
1.1
通讯作者：
J. Shao;H. Shan;Baofeng Wu
中科院分区：
文献类型：
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作者：
J. Shao;H. Shan;Baofeng Wu
一个非一致超图称为奇二部超图，如果是偶超图，且存在一个真子集，使得中的每条边包含奇数个顶点。奇二部超图是普通二部图的推广。研究了连通奇二部超图的谱性质。证明了连通一致超图的拉普拉斯H-谱与无号拉普拉斯H-谱相等的充要条件是连通一致超图是偶超图，是奇偶超图。我们进一步给出了连通奇二部超图的几个谱刻画。给出了连通一致超图的Laplacian谱半径与无号Laplacian谱半径相等的一个刻划，从而回答了L.气通过证明两个奇二部一致超图的笛卡尔积仍然是奇二部的，我们确定了当和都是连通的奇二部超图时，的拉普拉斯谱半径是和的拉普拉斯谱半径之和.
A -uniform hypergraph is called odd-bipartite, if is even and there exists some proper subset of such that each edge of contains odd number of vertices in . Odd-bipartite hypergraphs are generalizations of the ordinary bipartite graphs. We study the spectral properties of the connected odd-bipartite hypergraphs. We prove that the Laplacian H-spectrum and signless Laplacian H-spectrum of a connected -uniform hypergraph are equal if and only if is even and is odd-bipartite. We further give several spectral characterizations of the connected odd-bipartite hypergraphs. We also give a characterization for a connected -uniform hypergraph whose Laplacian spectral radius and signless Laplacian spectral radius are equal; thus, provide an answer to a question raised by L. Qi. By showing that the Cartesian product of two odd-bipartite -uniform hypergraphs is still odd-bipartite, we determine that the Laplacian spectral radius of is the sum of the Laplacian spectral radii of and , when and are both connected odd-bipartite.