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math.CO2025
The -core of a graph and its high-order spectra
Chunmeng Liu, Qing Xu, Changjiang Bu
The -core of a graph is its largest subgraph with minimum degree at least , a fundamental concept for uncovering hierarchical structures. In this paper, we establish a connec…
math.CO2025
The characteristic polynomial of sunflowers
Changjiang Bu, Lixiang Chen, Ge Lin
A uniform hypergraph is called a sunflower if all of its hyperedges intersect in the same set of vertices. In this paper, we determine the eigenvalues and spectral moments of a sun…
math.CO2025
On the second-largest modulus among the eigenvalues of a power hypergraph
Changjiang Bu, Lixiang Chen, Yongtang Shi
It is well known that the algebraic multiplicity of an eigenvalue of a graph (or real symmetric matrix) is equal to the dimension of its corresponding linear eigen-subspace, also k…