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Let $G = (V, E)$ be an undirected finite connected graph. Let $u$ be a specified vertex of $G$. Then the sum of distances $$ \sum_{v \in V} d_G(u,v) $$ is defined. Now we want to decrease this value, ...

This is a follow-up to my previous MO question: A discrete optimization problem related to the AM-GM inequality Let $n,k$ be integers such that $1\le k\le n$. Define the quantity $$ P(n,k):=\max\ a_1\...

Consider simple connected undirected graphs $G = (V, E)$ equipped with a function $w\colon E\rightarrow \{x\in \mathbb{R}\colon x\geq 0\}$. Define a function $d_{G,w}\colon V\times V\rightarrow\...