For a hypergraph H, let B(H) be its incidence matrix. The signless Laplacian matrix \(Q(H)=B(H)B(H)^T\), whose (i, j)-element is exactly the number of edges containing vertices \(v_i\) and \(v_j\) for \(i\ne j\) and (i, i)-element is exactly the degree of vertex \(v_i\). The incidence Q-tensor \({\mathcal {Q}}^*=B(H){\mathcal {I}}B(H)^T\), whose \((i_1,i_2,\ldots ,i_k)\)-entry of \({\mathcal {Q}}^*\) is exactly equal to the number of edges e of H satisfying \(i_t\in e\) for all \(t\in [k]\). Obviously, we can see more complete structural properties of H from \({\mathcal {Q}}^*\) than Q(H). Up to now, few tensors whose entries are directly related to structural properties of the corresponding hypergraphs. In this regard, we believe that it deserve to study the structural properties of hypergraphs though this tensor. In this paper, we will study some upper bounds on the spectral radius of \({\mathcal {Q}}^*\) by some parameters on hypergraphs.

对于超图H，令B（H）为其入射矩阵。无符号拉普拉斯矩阵\（Q（H）= B（H）B（H）^ T \），其（i，  j）元素正好是包含顶点\（v_i \）和\（v_j \ ）对于\（i \ ne j \）和（i，  i）元素正好是顶点\（v_i \）的度数。入射Q张量\（{\ mathcal {Q}} ^ * = B（H）{\ mathcal {I}} B（H）^ T \），其\（（i_1，i_2，\ ldots，i_k） \） - \（{\ mathcal {Q}} ^ * \）的条目正好等于边缘的数量Ë的ħ满足\（I_T \在电子\）对所有\（T \在[K] \） 。显然，我们可以看到更完整的结构特性^ h从\（{\ mathcal {Q} ^ * \）比Q（^ h）。到目前为止，几乎没有张量的条目直接与对应的超图的结构特性有关。在这方面，我们认为值得通过该张量来研究超图的结构特性。在本文中，我们将通过超图上的一些参数研究\（{\ mathcal {Q}} ^ * \）的光谱半径的一些上限。