DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

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Discussiones Mathematicae Graph Theory

Article in press


Authors:

H. Guo and B. Zhou

Title:

On the $\alpha$-spectral radius of uniform hypergraphs

Source:

Discussiones Mathematicae Graph Theory

Received: 2018-08-14, Revised: 2019-04-24, Accepted: 2019-04-24, https://doi.org/10.7151/dmgt.2268

Abstract:

For $0\le\alpha<1$ and a uniform hypergraph $G$, the $\alpha$-spectral radius of $G$ is the largest $H$-eigenvalue of $\alpha \mathcal{D}(G) +(1-\alpha) \mathcal{A}(G)$, where $\mathcal{D}(G)$ and $\mathcal{A}(G)$ are the diagonal tensor of degrees and the adjacency tensor of $G$, respectively. We give upper bounds for the $\alpha$-spectral radius of a uniform hypergraph, propose some transformations that increase the $\alpha$-spectral radius, and determine the unique hypergraphs with maximum $\alpha$-spectral radius in some classes of uniform hypergraphs.

Keywords:

$\alpha$-spectral radius, $\alpha$-Perron vector, adjacency tensor, uniform hypergraph, extremal hypergraph

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