3 problems

Let $T$ be a tree of order $n$, and let $I_{ecc}(T)$ denote its eccentricity-entropy. The diameter-three tree conjecture. Among trees of order $n$, the maximum value of $I_{ecc}$ i…

Let $G$ be a graph of order $n$, and let $I_{ecc}(G)$ denote its eccentricity-entropy. An extremal graph is one attaining the minimum value of this entropy. The minimum eccentricit…

Wiener–eccentricity monotonicity conjecture. For every such edge $e$,