The (signless Laplacian) spectral radius (of subgraphs) of uniform hypergraphs

Abstract

Let λ 1 (G) and q 1 (G) be the spectral radius and the signless Laplacian spectral radius of a kuniform hypergraph G, respectively. In this paper, we give the lower bounds of d − λ 1 (H) and 2d − q 1 (H), where H is a proper subgraph of a f (-edge)-connected d-regular (linear) k-uniform hypergraph. Meanwhile, we also give the lower bounds of 2∆ − q 1 (G) and ∆ − λ 1 (G), where G is a nonregular f (-edge)-connected (linear) k-uniform hypergraph with maximum degree ∆.

Some Properties of the Signless Laplacian and Normalized Laplacian Tensors of General Hypergraphs

“…Liu et al [15] investigated the bounds of the principal ratio γ(H) = x max /x min and gave an estimate of the gap of spectral radii between H and its proper sub-hypergraph H . Many scholars also started to investigate the signless Laplacian spectral radius of m-uniform hypergraphs [7,14,25].…”

The bounds of the spectral radius of general hypergraphs in terms of clique number

“…Recently, spectral hypergraph theory develops rapidly. There are many work about the spectral theory of hypergraphs [4,5,6,14,21,22]. However, there are still few studies the relation bewteen the clique number and the (signless Laplacian) spectral radius of hypergraphs.…”