5 problems

Let $G$ be a graph of order $n$, and let $W(G)$ denote the sum of distances between all unordered pairs of vertices. For positive integers $n$ and $r$ satisfying $n\ge 2r$ and…

Let $G$ be a connected graph. Its average eccentricity is the arithmetic mean of the eccentricities of its vertices, and its remoteness is the maximum average distance from a verte…

Let $D$ be a digraph of order $n$, and let $W(D)$ denote the sum of distances over all ordered pairs of vertices. The outradius of $D$ is the least integer $r$ for which some verte…

Let $G$ be a $delta$-regular graph of order $n$, meaning that every vertex of $G$ has degree $delta$. Let $\mu(G)$ denote the average distance between unordered pairs of vertices o…

Let $n$ and $r$ be two positive integers with $n \ge 2r$ and $r \ge 3$. For a digraph $D$, let $W(D)$ denote the sum of distances over all ordered pairs of vertices, let the outrad…