Largest <Emphasis Type="Italic">H</Emphasis>-eigenvalue of uniform <Emphasis Type="Italic">s</Emphasis>-hypertrees |
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Authors: | Yuan Hou An Chang Lei Zhang |
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Institution: | 1.Center for Discrete Mathematics and Theoretical Computer Science,Fuzhou University,Fuzhou,China;2.Department of Computer Engineering,Fuzhou University Zhicheng College,Fuzhou,China |
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Abstract: | The k-uniform s-hypertree G = (V,E) is an s-hypergraph, where 1 ≤ s ≤ k - 1; and there exists a host tree T with vertex set V such that each edge of G induces a connected subtree of T. In this paper, some properties of uniform s-hypertrees are establised, as well as the upper and lower bounds on the largest H-eigenvalue of the adjacency tensor of k-uniform s-hypertrees in terms of the maximal degree Δ. Moreover, we also show that the gap between the maximum and the minimum values of the largest H-eigenvalue of k-uniform s-hypertrees is just Θ(Δ s/k ). |
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