The effect on the (signless Laplacian) spectral radii of uniform hypergraphs by subdividing an edge

Abstract In this paper, we investigate how the spectral radius (resp., signless Laplacian spectral radius) changes when a connected uniform hypergraph is perturbed by subdividing an edge. We extend the results of Hoffman and Smith from connected graphs to connected uniform hypergraphs. Moreover, we also study how the Laplacian spectral radius behaves when an odd-bipartite uniform hypergraph is perturbed by subdividing an edge. As applications, we determine the unique unicyclic hypergraph with the largest signless Laplacian spectral radius, and also determine the unique unicyclic even uniform hypergraph with the largest Laplacian spectral radius.

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