Inverse Perron Values and Connectivity of a Uniform Hypergraph

  • Changjiang Bu
  • Haifeng Li
  • Jiang Zhou
Keywords: Hypergraph, Inverse Perron value, Laplacian tensor, Connectivity


In this paper, we show that a uniform hypergraph $\mathcal{G}$ is connected if and only if one of its inverse Perron values is larger than $0$. We give some bounds on the bipartition width, isoperimetric number and eccentricities of $\mathcal{G}$ in terms of inverse Perron values. By using the inverse Perron values, we give an estimation of the edge connectivity of a $2$-design, and determine the explicit edge connectivity of a symmetric design. Moreover, relations between the inverse Perron values and resistance distance of a connected graph are presented.



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