The relationship between the tensor spectrum and structural parameters of hypergraphs is a hot topic in the field of hypergraph theory in recent years. This work first establishes the relation between the $ \alpha $-spectral radius and diameter for $ s $-uniform hypergraphs of a given order. Second, we obtain the relation between $ \alpha $-spectral radius, connectivity and independence number of $ 3 $-uniform hypergraphs with given order. Additionally, the extremal structure achieving the maximum $ \alpha $-spectral radius is characterized for supertrees, specifically through the difference between the maximum degree and its $ \alpha $-spectral radius.
Citation: Qiannan Niu, Lei Zhang, Haizhen Ren. The relation between $ \alpha $-spectral radius and structure parameters of $ s $-uniform hypergraphs[J]. AIMS Mathematics, 2026, 11(9): 27689-27705. doi: 10.3934/math.20261107
The relationship between the tensor spectrum and structural parameters of hypergraphs is a hot topic in the field of hypergraph theory in recent years. This work first establishes the relation between the $ \alpha $-spectral radius and diameter for $ s $-uniform hypergraphs of a given order. Second, we obtain the relation between $ \alpha $-spectral radius, connectivity and independence number of $ 3 $-uniform hypergraphs with given order. Additionally, the extremal structure achieving the maximum $ \alpha $-spectral radius is characterized for supertrees, specifically through the difference between the maximum degree and its $ \alpha $-spectral radius.
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Qiannan Niu, Lei Zhang, Haizhen Ren. The relation between $ \alpha $-spectral radius and structure parameters of $ s $-uniform hypergraphs[J]. AIMS Mathematics, 2026, 11(9): 27689-27705. doi: 10.3934/math.20261107
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