纯粹数学与应用数学
純粹數學與應用數學
순수수학여응용수학
PURE AND APPLIED MATHEMATICS
2014年
6期
581-586
,共6页
一致超图%张量%谱半径%界
一緻超圖%張量%譜半徑%界
일치초도%장량%보반경%계
uniform hypergraph%tensor%spectral radius%bound
利用张量理论研究一致超图的谱半径。首先，利用对角相似张量与原张量同谱的性质，结合张量特征值的圆盘定理，给出谱半径的上界，这一上界严格小于最大度；其次，通过超图的度向量给出谱半径的下界。改进了超图谱半径上下界的原有结果。
利用張量理論研究一緻超圖的譜半徑。首先，利用對角相似張量與原張量同譜的性質，結閤張量特徵值的圓盤定理，給齣譜半徑的上界，這一上界嚴格小于最大度；其次，通過超圖的度嚮量給齣譜半徑的下界。改進瞭超圖譜半徑上下界的原有結果。
이용장량이론연구일치초도적보반경。수선，이용대각상사장량여원장량동보적성질，결합장량특정치적원반정리，급출보반경적상계，저일상계엄격소우최대도；기차，통과초도적도향량급출보반경적하계。개진료초도보반경상하계적원유결과。
In this paper, the spectral radius of a uniform hypergraph is studied according to properties of tensors. Firstly, based on Gerschgorin′s theorem and the property that two diagonal similar tensors have the same spectrum, an upper bound for the spectral radius is given. This bound is strictly less than the maximum degree of the hypergraph. Secondly, a lower bound for the spectral radius is introduced by using the degree vector of the hypergraph. These bounds are improvements of the original results.
