Abstract:

In this paper, we extend the concepts of inverse Perron values to general hypergraphs. We show that a general hypergraph $\mathcal{G}$ is connected if and only if any inverse Perron values is large than 0. We give some bounds on the bipartition width, isoperimetric number, eccentricities and degrees of a hypergraph $\mathcal{G}$ in terms of inverse Perron values. Finally, we obtain that a weakly irreducible, nonnegative, symmetric tensor $A$ is odd-colorable if and only if its Laplacian tensor and the signless Laplacian tensor have the same spectral.

Key words: hypergraph, analytic connectivity, Inverse Perron value, Odd-colorable