This partial list of

graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ...

s contains definitions of graphs and graph families which are known by particular names, but do not have a Wikipedia article of their own. For collected definitions of

graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...

terms that do not refer to individual graph types, such as ''vertex'' and ''path'', see Glossary of graph theory. For links to existing articles about particular kinds of graphs, see Graphs.

Gear

A gear graph, denoted ''G''_''n'' is a graph obtained by inserting an extra vertex between each pair of adjacent vertices on the perimeter of a

wheel graph A wheel is a circular component that is intended to rotate on an axle bearing. The wheel is one of the key components of the wheel and axle which is one of the six simple machines. Wheels, in conjunction with axles, allow heavy objects to be ...

''W''_''n''. Thus, ''G''_''n'' has 2''n''+1 vertices and 3''n'' edges. Gear graphs are examples of

squaregraph In graph theory, a branch of mathematics, a squaregraph is a type of undirected graph that can be drawn in the plane in such a way that every bounded face is a quadrilateral and every vertex with three or fewer neighbors is incident to an unbound ...

s, and play a key role in the

forbidden graph characterization In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to the family and further exclude all graphs from the family which contain any of these forbidde ...

of squaregraphs. Gear graphs are also known as cogwheels and bipartite wheels.

Helm

A helm graph, denoted ''H_n'' is a graph obtained by attaching a single edge and node to each node of the outer circuit of a

''W_n''.

Lobster

A lobster graph is a

tree In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are ...

in which all the vertices are within distance 2 of a central

path A path is a route for physical travel – see Trail. Path or PATH may also refer to: Physical paths of different types * Bicycle path * Bridle path, used by people on horseback * Course (navigation), the intended path of a vehicle * Desire p ...

. Compare ''caterpillar''.

Web

The web graph ''W''_''n'',''r'' is a graph consisting of ''r'' concentric copies of the

cycle graph In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices (at least 3, if the graph is simple) connected in a closed chain. The cycle graph with vertices is called ...

''C''_''n'', with corresponding vertices connected by "spokes". Thus ''W''_''n'',1 is the same graph as ''C''_''n'', and ''W''_n,2 is a

prism Prism usually refers to: * Prism (optics), a transparent optical component with flat surfaces that refract light * Prism (geometry), a kind of polyhedron Prism may also refer to: Science and mathematics * Prism (geology), a type of sedimentary ...

. A web graph has also been defined as a prism graph ''Y''_{''n''+1, 3}, with the edges of the outer cycle removed.

References

{{DEFAULTSORT:Graphs Mathematics-related lists * *

Gear

Helm

Lobster

Web

See also

References