Gear graph
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 about particular kinds of graphs, see Category:Graphs.
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. Gear graphs are examples of squaregraphs, and play a key role in the forbidden graph characterization of squaregraphs. Gear graphs are also known as cogwheels and bipartite wheels.
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.
A helm graph, denoted Hn is a graph obtained by attaching a single edge and node to each node of the outer circuit of a wheel graph Wn.
A lobster graph is a tree in which all the vertices are within distance 2 of a central path. Compare caterpillar.
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