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.
