Exact Power of Trees

Student: Nikita Manuylenko

Educational Programme: Modern Computer Science (Master)

Year of Graduation: 2024

Given a graph $G$, the exact-distance cube $G^{[\#3]}$ of $G$ is a graph on vertex set $V(G)$, such that edge $(v_i, v_j)$ in $G^{[\#3]}$ exists if and only if distance between $v_i$ and $v_j$ in $G$ is exactly 3. Graph $G$ is called exact cube root of $G^{[\#3]}$. In our study, we provide linear-time algorithm to check if given tree or forest graph $G$ has a tree exact cube root. We also provide partial structural analysis that may help us expand those results onto the general case of all graphs $G$.

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