arXiv subjects
Publications and source records attributed to M. J. Moghaddamzadeh.
For a graph $G$, let $λ_2(G)$ denote its second smallest Laplacian eigenvalue. It was conjectured that $λ_2(G) + λ_2(\overline G) \ge 1$, where $\overline G$ is the complement of $G$. In this paper, it is shown that $\max\{λ_2(G), λ_2(\overline G)\} \ge 2/5$.
The notion of acyclic matching property was provided by Losonczy and it was proved that torsion-free groups admit this property. In this paper, we introduce a duality of acyclic matching as a tool for classification of some Abelian groups, moreover, we study matchings for vector spaces and give a connection between matchings in groups and vector spaces. Our tools mix additive number theory, combinatorics and algebra.