Abstract
A supertree is a connected and acyclic hypergraph. Let be the set of the r-uniform supertrees with m edges and exactly two vertices of maximum degree ▵, where and . We investigate the supertree with the minimum spectral radius among . Several useful grafting operations are introduced for comparing the spectral radii of supertrees. The supertree with the minimum spectral radius among is characterized. In addition, a new simple method is demonstrated to obtain the supertree with the minimum spectral radius among the set of r-uniform supertrees with m edges.
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