Geodesic
Inverse Perron values and connectivity of a uniform hypergraph
The electronic journal of combinatorics, Tome 25 (2018) no. 4
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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.
DOI : 10.37236/7410
Classification : 05C50, 05C65, 05C40
Mots-clés : hypergraph, inverse Perron value, Laplacian tensor, connectivity 
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     author = {Changjiang Bu and Haifeng Li and Jiang Zhou},
     title = {Inverse {Perron} values and connectivity of a uniform hypergraph},
     journal = {The electronic journal of combinatorics},
     year = {2018},
     volume = {25},
     number = {4},
     doi = {10.37236/7410},
     zbl = {1402.05134},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/7410/}
}
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Changjiang Bu; Haifeng Li; Jiang Zhou. Inverse Perron values and connectivity of a uniform hypergraph. The electronic journal of combinatorics, Tome 25 (2018) no. 4. doi: 10.37236/7410

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