6 problems

Let $a\from (2,5/2)$, let $\bigl(f_i\bigr)_{i\geq 1}$ be the sampled marked vertices or faces, let $d^\dagger_\mathrm{gr}$ denote the graph distance, and let…

For a positive integer $d$, a distance-$d$ packing of cycles in a graph $G$ is a set of cycles such that no path of length at most $d$ joins two distinct cycles. For a vertex set…

Maximum-diameter conjecture. The maximum diameter of such a graph is

Let $T$ and $T'$ be any two trees with $n$ vertices. Randić–degree-power entropy distance conjecture. It holds … Here $R$ is the Randić index and $If_1$ is the degree-power entropy…

Let $T$ and $T'$ be any two trees with $n$ vertices. Energy–graph-entropy distance conjecture. It holds … Here $E$ is the graph energy and $Ig$ is the entropy based on the absolute…

Let $T$ and $T'$ be any two trees with $n$ vertices. Wiener–Randić distance conjecture. It holds … The conjecture compares graph distance measures induced by the Wiener and Randić…