Fan graph
In graph theory, a fan graph is a graph formed by the join of a path graph and an empty graph on a single vertex. The fan graph on vertices, denoted, is defined as, where is a single vertex and is a path on vertices.
The fan graph has vertices and edges.
Saturation
A graph is -saturated if it does not contain as a subgraph, but the addition of any edge results in at least one copy of as a subgraph. The saturation number is the minimum number of edges in an -saturated graph on vertices, while the extremal number is the maximum number of edges possible in a graph on vertices that does not contain a copy of.The -fan,, is the graph consisting of edge-disjoint triangles that intersect at a single vertex.
The saturation number for is for and.