8 problems

Sign conjecture. For any tree on $n$ vertices,

Let $G$ be a connected graph of order at least $k$, and let $\operatorname{srad}_k(G)$ and $\operatorname{sdiam}_k(G)$ denote its Steiner $k$-radius and Steiner $k$-diameter, respe…

Let $n$, $k$, and $k^{\prime}$ be integers with $n\geq k\geq3$ and $k>k^{\prime}\geq1$, and let $T$ be a tree with order $n$. The Steiner diameter–radius conjecture. … The paper pr…

Let $T$ be a tree on $n$ vertices, and let $k$ be a positive integer. The $k$-Steiner distance hyperdeterminant is the hyperdeterminant of the $k$-th order Steiner distance hyperma…

Let $T$ be a tree on $n$ vertices, and let $k$ be the order of its Steiner distance hypermatrix. The hyperdeterminant is a function only of $n$, independent of the isomorphism type…

Let $G$ be a connected graph of order $n\geq k$, and let $\mu(G)$ denote its average distance and $\mu_k(G)$ its average Steiner $k$-distance. Dankelmann–Oellermann–Swart conjectur…

Let $C_n^{2k}$ denote the $2k$-th power of the cycle $C_n$. Let $G$ be a $2k$-connected graph of order $n$. Dankelmann–Swart–Oellermann conjecture. … This conjectures that the $2k$…

Let $k\geq 2$ be an integer, and let $G$ be a connected graph of order $n\geq k$. The Steiner $k$-diameter $\operatorname{sdiam}_k(G)$ is the maximum Steiner distance over all $k$-…