arXiv subjects

Miriam Abdón

Publications and source records attributed to Miriam Abdón.

2 recordsLinked to original sources

arXiv2026

On the spectra of k-uniform threshold hypergraphs

In this article we introduce a definition of k-uniform thresholds hypergraphs through a binary sequence, a natural extension of the classical definition for thresholds graphs. We characterize some of its eigenvalues and multiplicities by means of combinatorial numbers, derived from edge counts. An important problem addressed in Spectral Graph Theory is to find graphs with few distinct eigenvalues. Our characterization allows us to construct k-uniform threshold hypergraphs having an arbitrary number of vertices with few distinct eigenvalues.

math.CO↗

arXiv2026

Characterizing graphs with the second largest distance eigenvalue less than -1/2

Let $G$ be a connected graph with vertex set $V$. The distance, $d_G(u, v)$, between vertices $u$ and $v$ of $G$ is defined as the length of a shortest path between $u$ and $v$ in $G$. The distance matrix of $G$ is the matrix $\mathbf{D}(G) =[d_G(u, v)]_{u,v\in V}$. The second largest distance eigenvalue $λ_2(G)$ of $G$ is the second largest one in the spectrum of $\mathbf{D}(G)$. In this work, we completely characterize the connected graphs $G$ for which $λ_2(G)<-1/2$ through approaches both spectral and structural.

math.CO↗