Gallery of named graphs

Some of the finite structures considered in graph theory have names, sometimes inspired by the graph's topology, and sometimes after their discoverer. A famous example is the Petersen graph, a concrete graph on 10 vertices that appears as a minimal example or counterexample in many different contexts.

Individual graphs

Graph families

trongly regular graph

The strongly regular graph on "v" vertices and rank "k" is usually denoted srg("v,k",λ,μ).The picture of Clebsch graph is incorrect and should be replaced (see http://arxiv.org/abs/math/0602580v1 or http://mathworld.wolfram.com/ClebschGraph.html).

Complete graphs

The complete graph on $n$ vertices is often called the "$n$-clique" and usually denoted $K\_n$, from German "komplett". Fact|date=February 2007

Complete bipartite graphs

The complete bipartite graph is usually denoted $K\_\{n,m\}$

Platonic solids

The complete graph on four vertices forms the skeleton of the tetrahedron, and more generally the complete graphs form skeletons of simplices. The hypercube graphs are also skeletons of higher dimensional regular polytopes.

Cycles

The cycle graph on $n$ vertices is called the "n-cycle" and usually denoted $C\_n$. It is also called a "cyclic graph", a "polygon" or the "n-gon". Special cases are the "triangle" $C\_3$, the "square" $C\_4$, and the "pentagon" $C\_5$.

tar

A star "S"_k is the complete bipartite graph "K"_1,"k".

Wheel

The wheel graph "W_n" is a graph on "n" vertices constructed by connecting a single vertex to every vertex in an ("n"-1)-cycle.

Fullerene graphs

In graph theory, the term fullerene refers to any 3-regular, planar graph with all faces of size 5 or 6 (including the external face). It follows from Euler's polyhedron formula, $V-E+F\; =\; 2,$ (where $V,\; E,\; F\; ,$ indicate the number of vertices, edges, and faces), that there are exactly 12 pentagons in a fullerene and $V/2-10,$ hexagons. Fullerene graphs are the Schlegel representations of the corresponding fullerene compounds.