Let ${\mathbb{B}}_{n,k,a}$ be the set of weighted k-uniform connected bicyclic hypergraphs of order n with positive integer weights and fixed total weight sum a, where n, k and a are positive integers with $k\ge 4$ and $a\ge \frac{n+1}{k-1}\ge 3$. An α-normal labelling method is proposed for comparing the spectral radii of the weighted hypergraphs under consideration. The weighted hypergraph having the maximum spectral radius among the hypergraps in ${\mathbb{B}}_{n,k,a}$ is obtained.

中文翻译：

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加权双环超图的最大谱半径

让${\mathbb{乙}}_{n,k,A}$是具有正整数权重和固定总权重和a的n阶加权k -均匀连通双环超图的集合，其中n、k和a是正整数$k\ge \mathrm{4个}$和$A\ge \frac{n+\mathrm{1个}}{k-\mathrm{1个}}\ge \mathrm{3个}$. 提出了一种α-正态标记方法来比较所考虑的加权超图的谱半径。在超图中具有最大谱半径的加权超图${\mathbb{乙}}_{n,k,A}$获得。