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SQUAREGRAPH

Squaregraph

Planar graph with quadrilateral faces

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

Squaregraph

King's graph

Graph of king moves on a chessboard

generalization of the king's graph, called a kinggraph, is formed from a squaregraph (a planar graph in which each bounded face is a quadrilateral and each

King's graph

King's_graph

Median graph

Graph with a median for each three vertices

such a way that medians can be calculated coordinatewise in this way. Squaregraphs, planar graphs in which all interior faces are quadrilaterals and all

Median graph

Median_graph

List of graphs

Gear graphs are examples of squaregraphs, and play a key role in the forbidden graph characterization of squaregraphs. Gear graphs are also known as

List of graphs

List_of_graphs

Matchstick graph

Graph with edges of length one, able to be drawn without crossings

arbitrary tree as a matchstick graph. A similar property is true for squaregraphs, the planar graphs that can be drawn in the plane in such a way that

Matchstick graph

Matchstick_graph

Polyomino

Geometric shape formed from squares

representations of the symmetric group. Blokus, a board game using polyominoes. Squaregraph, a kind of undirected graph including as a special case the graphs of

Polyomino

Bipartite graph

Graph divided into two independent sets

even length is bipartite. Special cases of this are grid graphs and squaregraphs, in which every inner face consists of 4 edges and every inner vertex

Bipartite graph

Bipartite_graph

Glossary of graph theory

subgraph of its square induced by one side of the bipartition. 2. A squaregraph is a planar graph that can be drawn so that all bounded faces are 4-cycles

Glossary of graph theory

Glossary_of_graph_theory

Circle graph

Intersection graph of a chord diagram

triangle-free circle graphs is equivalent to the problem of representing squaregraphs as isometric subgraphs of Cartesian products of trees; in this correspondence

Circle graph

Circle_graph

Penny graph

Graph formed by touching unit circles

By arranging the pennies in a square grid, or in the form of certain squaregraphs, one can form triangle-free penny graphs whose number of edges is at

Penny graph

Penny_graph

Partial cyclic order

Eppstein, David (2010), "Combinatorics and geometry of finite and infinite squaregraphs" (PDF), SIAM Journal on Discrete Mathematics, 24 (4): 1399–1440, arXiv:0905

Partial cyclic order

Partial_cyclic_order

Partial cube

Isometric subgraph of a hypercube

graphs are examples of median graphs. Since the median graphs include the squaregraphs, simplex graphs, and Fibonacci cubes, as well as the covering graphs

Partial cube

Partial_cube