Author

R. Škrekovski

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Preprint Aug 2026

Resolutions of two conjectures on the spectral diameter

Let $\lambda_1(G) \geq \dots \geq \lambda_n(G)$ be the adjacency spectrum of a graph $G$ on $n$ vertices. The spectral distance $\sigma(G,H)$ between $n$-vertex graphs $G$ and $H$ is the Manhattan distance between their spectra, i.e. $\sigma(G,H) = \sum_{i=1}^n |\lambda_i(G) - \lambda_i(H)|$. Given a set $\mathcal{G}$...

Irena M. Jovanović, Jelena Sedlar, R. Škrekovski · 0 citations

Preprint Aug 2026

On the odd independence number of the Queen graph

A set S of vertices of a graph is odd independent if it is independent and every vertex outside S has either zero or an odd number of neighbors in S. The largest size of such a set is the odd independence number alpha_od. Caro, Petrusevski, Skrekovski and Tuza [2] conjectured that alpha_od = 1 for every finite Queen gr...

M. Knor, Jelena Sedlar, R. Škrekovski · 0 citations