Gallery of named graphs

From Wikipedia, the free encyclopedia

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.

1 Individual graphs
2 Graph families

[edit] Individual graphs

The following picture of Clebsch graph is not correct. It should be replaced (see http://arxiv.org/PS_cache/math/pdf/0602/0602580v1.pdf or http://mathworld.wolfram.com/ClebschGraph.html).

Clebsch graph	Desargues graph	Flower snark	Folkman graph
Gray graph	Grötzsch graph	Hall–Janko graph	Heawood graph
Möbius–Kantor graph	Pappus graph	Petersen graph	Shrikhande graph
Szekeres snark	Tutte eight-cage

[edit] Graph families

[edit] Complete graphs

The complete graph on $n$ vertices is often called the $n$ -clique and usually denoted $K n$ , from German komplett.^{[citation needed]}

$K 1$	$K 2$	$K 3$	$K 4$
$K 5$	$K 6$	$K 7$	$K 8$

[edit] Complete bipartite graphs

The complete bipartite graph is usually denoted $K n, m$

Claw $K 3,1$

$K 3,2$

$K 3,3$

[edit] 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.

Cube
$n = 8$ , $m = 12$

Octahedron
$n = 6$ , $m = 12$

Dodecahedron
$n = 20$ , $m = 30$

Icosahedron
$n = 12$ , $m = 30$

[edit] 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 $C 5$ .