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Erschienen in:
16.07.2019
The \(\alpha \)-spectral radius of uniform hypergraphs concerning degrees and domination number
Erschienen in: Journal of Combinatorial Optimization | Ausgabe 4/2019
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Abstract
For \(0\le \alpha <1\) and an r-uniform hypergraph H, the \(\alpha \)-spectral radius of H is the maximum modulus of eigenvalues of \(\alpha {\mathcal {D}}(H)+(1-\alpha ){\mathcal {A}}(H)\), where \({\mathcal {D}}(H)\) and \({\mathcal {A}}(H)\) are the diagonal tensor of degrees and the adjacency tensor of H, respectively. In this paper, we give a lower bound on the \(\alpha \)-spectral radius of a linear r-uniform hypergraph in terms of its domination number. Then, we obtain some bounds on the \(\alpha \)-spectral radius in terms of vertex degrees and we characterize the extremal hypergraphs attaining the bound.