A fan graph 
is defined as the graph join 
,
where 
is the empty
graph on 
vertices and 
is the path graph on 
vertices.
The case 
corresponds to the usual fan graphs, while 
corresponds to the double fan, etc. Precomputed properties
of fan graphs are implemented in the Wolfram
Language as GraphData[{"Fan",
{m, n}}].
The 
-fan graph is isomorphic to the complete tripartite graph 
,
and the 
-fan
graph to 
.
The fan graph 
is sometimes known as the gem graph.
