List of graphs
From Wikipedia, the free encyclopedia
This partial list of graphs 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 terms that do not refer to individual graph types, such as vertex and path, see Glossary of graph theory. For links to existing articles on graph theory, see List of graph theory topics, Category:Graphs, and Category:Graph families.
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[edit] Caterpillar
A caterpillar graph, or caterpillar tree, is a tree such that if all leaf vertices and their incident edges are removed, the remainder of the graph forms a path. In other words, all the vertices of a caterpillar are within distance 1 of a central path.
Alternatively, A caterpillar is a tree in which every graph vertex is on a central stalk or only one graph edge away from the stalk (in other words, removal of its endpoints leaves a path graph; Gallian 2007).A tree is a caterpillar iff all nodes of degree >=3 are surrounded by at most two nodes of degree two or greater.
examples: "http://mathworld.wolfram.com/images/eps-gif/CaterpillarTrees_800.gif"
Compare lobster.[1]
[edit] Gear
A gear graph, denoted Gn is a graph obtained by inserting an extra vertex between each pair of adjacent vertices on the perimeter of a wheel graph Wn. Thus, Gn has 2n+1 vertices and 3n edges.[2]
[edit] Grid
A grid graph is a unit distance graph corresponding to the square lattice, so that it is isomorphic to the graph having a vertex corresponding to every pair of integers (a, b), and an edge connecting (a, b) to (a+1, b) and (a, b+1). The finite grid graph Gm,n is an m×n rectangular graph isomorphic to the one obtained by restricting the ordered pairs to the range 0 ≤ a < m, 0 ≤ b < n. Grid graphs can be obtained as the Cartesian product of two paths: Gm,n = Pm × Pn. Every grid graph is a median graph.[3]
[edit] Filmstrip
A filmstrip graph can be obtained as the Cartesian product of two paths, one of which has only one edge: Gm,1 = Pm × P1.
[edit] Lobster
A lobster graph is a graph in which all the vertices are within distance 2 of a central path; compare caterpillar.[4]
[edit] Web
The web graph Wn,r is a graph consisting of r concentric copies of the cycle graph Cn, with corresponding vertices connected by "spokes". Thus Wn,1 is the same graph as Cn, and Wn,2 is a prism.[5]
