---
tag: YXXV9S2DKD
kind: concept
name: Triameter (graph theory)
sources:
  - wikipedia: en:79699840@r1317724680
    locator: Triameter (graph theory)
    note: adopted
    mention: wikipedia://en/79699840
    sections: [Summary]
same_as:
  wikidata: Q133886647
  wikipedia: Triameter (graph theory)
inventory: [N6Q88M3V1H]
---

## Summary

In graph theory, the **triameter** is a metric invariant that generalizes the concept of a graph's diameter. It is defined as the maximum sum of pairwise [[distances|0QV9VNNB4Z]] between any three vertices in a connected graph $G$ and is denoted by

$$\mathop{\mathrm{tr}}(G) = \max\{d(u,v) + d(v,w) + d(u,w) \mid u,v,w \in V\},$$

where $V$ is the vertex set of $G$ and $d(u,v)$ is the length of the shortest [[path|03NAMV1DHJ]] between vertices $u$ and $v$.