The triangle graph is the cycle graph 
, which is isomorphic to the complete
graph 
as well as to the complete tripartite graph 
and the triangular
snake graph 
.
The triangle graph is the line graph of both the claw graph and itself. It is a rigid graph.
The term "triangle graph" is also used to refer to any triangular graph, of which the usual triangle graph is the simplest case.
A 
subgraph of a graph is called a graph triangle.
