Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/8336
Title: The extremal spectral radii of k-uniform supertrees
Authors: Li, H
Shao, JY
Qi, LQ 
Keywords: Adjacency tensor
Hypergraph
Incidence $$Q$$Q-tensor
Signless Laplacian tensor
Spectral radius
Supertree
Issue Date: 2015
Publisher: Kluwer Academic Publishers
Source: Journal of combinatorial optimization, 2015 How to cite?
Journal: Journal of Combinatorial Optimization 
Abstract: In this paper, we study some extremal problems of three kinds of spectral radii of (Formula presented.)-uniform hypergraphs (the adjacency spectral radius, the signless Laplacian spectral radius and the incidence (Formula presented.)-spectral radius). We call a connected and acyclic (Formula presented.)-uniform hypergraph a supertree. We introduce the operation of “moving edges” for hypergraphs, together with the two special cases of this operation: the edge-releasing operation and the total grafting operation. By studying the perturbation of these kinds of spectral radii of hypergraphs under these operations, we prove that for all these three kinds of spectral radii, the hyperstar (Formula presented.) attains uniquely the maximum spectral radius among all (Formula presented.)-uniform supertrees on (Formula presented.) vertices. We also determine the unique (Formula presented.)-uniform supertree on (Formula presented.) vertices with the second largest spectral radius (for these three kinds of spectral radii). We also prove that for all these three kinds of spectral radii, the loose path (Formula presented.) attains uniquely the minimum spectral radius among all (Formula presented.)-th power hypertrees of (Formula presented.) vertices. Some bounds on the incidence (Formula presented.)-spectral radius are given. The relation between the incidence (Formula presented.)-spectral radius and the spectral radius of the matrix product of the incidence matrix and its transpose is discussed.
URI: http://hdl.handle.net/10397/8336
ISSN: 1382-6905
DOI: 10.1007/s10878-015-9896-4
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