List of graphs

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.

The strongly regular graph on v vertices and rank k is usually denoted srg(v,k,λ,μ).

A symmetric graph is one in which there is a symmetry (graph automorphism) taking any ordered pair of adjacent vertices to any other ordered pair; the Foster census lists all small symmetric 3-regular graphs.

Every strongly regular graph is symmetric, but not vice versa.

It is also called a cyclic graph, a polygon or the n-gon.

[2] 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 h = V/2 – 10 hexagons.

An algorithm to generate all the non-isomorphic fullerenes with a given number of hexagonal faces has been developed by G. Brinkmann and A.

[3] G. Brinkmann also provided a freely available implementation, called fullgen.

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.

The smallest snark is the Petersen graph, already listed above.

A star Sk is the complete bipartite graph K1,k.

[4] Gear graphs are examples of squaregraphs, and play a key role in the forbidden graph characterization of squaregraphs.

[5] Gear graphs are also known as cogwheels and bipartite wheels.

[6][7] A lobster graph is a tree in which all the vertices are within distance 2 of a central path.