A fan graph
is defined as the graph join
, where
is the empty graph on
nodes and
is the path graph on
nodes. 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.