The diamond graph has radius 1, diameter 2, girth 3, chromatic number 3 and chromatic index 3.

A graph is diamond-free if it has no diamond as an induced subgraph.

Alternatively, a graph is diamond-free if and only if every pair of maximal cliques in the graph shares at most one vertex.

This graph family may be characterized by a single forbidden minor.

The characteristic polynomial of the diamond graph is ⁠