Author

Zhan-He Zhang

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Preprint Oct 2026

Spectral Extremal 1-Planar Graphs with Bounded Pentagon Packing

Let $\mathcal P_1$ denote the class of 1-planar graphs and let $tC_5$ be the disjoint union of $t$ copies of $C_5$. For every fixed $t\ge3$ and all sufficiently large $n$, we determine the unique $n$-vertex $tC_5$-free graph in $\mathcal P_1$ with maximum adjacency spectral radius, answering Problem 1 of Li, Wang and Z...

Zhan-He Zhang · 0 citations

Preprint Oct 2026

Regular $K_3$-Irregular Graphs of Every Regularity at Least Nine

For a vertex $v$ of a graph $G$, the triangle-degree $\operatorname{td}_G(v)$ is the number of triangles containing $v$. A graph is triangle-distinct, or $K_3$-irregular, if its vertex triangle-degrees are pairwise distinct. Chartrand, Erd\H{o}s, and Oellermann asked whether a regular $K_3$-irregular graph exists. We p...

Zhan-He Zhang · 1 citation · ⚡1