Oleksiy Al-saadi

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20242026

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math.CO2026

A Spanning Subgraph of Conway's 99-graph

Joseph Natal, Oleksiy Al-saadi

We show that in any hypothetical $G$ = srg(99,14,1,2) a spanning subgraph with $189$ edges is forced. Moreover, the graph formed out of the remaining edges has the spectrum $(12^1,…

math.CO2026

On the Periodicity of k-distance Graphs

Gregory Demo, David Lund, Oleksiy Al-saadi

The $k$ -distance graph $G^{k}$ of a graph $G$ has the same vertex set as $G$ and two vertices are adjacent if and only if their distance is $k$ in $G$ . These graphs have been extensi…

math.CO2025

Diameter Constraints in 2-distance Graphs

Oleksiy Al-saadi, Joseph Natal

For any finite, simple graph $G = (V, E)$ , its $2$ -distance graph $G_{2}$ is a graph having the same vertex set $V$ where two vertices are adjacent if and only if their distance is $2…