Fan Graph


A fan graph F_(m,n) is defined as the graph join K^__m+P_n, where K^__m is the empty graph on m nodes and P_n is the path graph on n nodes. The case m=1 corresponds to the usual fan graphs, while m=2 corresponds to the double fan, etc. Precomputed properties of fan graphs are implemented in the Wolfram Language as GraphData[{"Fan", {m, n}}].

The (r,2)-fan graph is isomorphic to the complete tripartite graph K_(1,1,r), and the (r,3)-fan graph to K_(1,2,r).

The fan graph F_(4,1) is sometimes known as the gem graph.

See also

Complete Tripartite Graph, Gem Graph

Explore with Wolfram|Alpha


Brandstädt, A.; Le, V. B.; and Spinrad, J. P. Graph Classes: A Survey. Philadelphia, PA: SIAM, p. 18, 1987.Gallian, J. "Dynamic Survey of Graph Labeling." Elec. J. Combin. DS6. Dec. 21, 2018.

Referenced on Wolfram|Alpha

Fan Graph

Cite this as:

Weisstein, Eric W. "Fan Graph." From MathWorld--A Wolfram Web Resource.

Subject classifications