# What are graphs?

### Some articles on graphs, graph:

Squaregraph - Related Graph Classes
... include as special cases trees, grid graphs, gear graphs, and the graphs of polyominos ... As well as being planar graphs, squaregraphs are median graphs, meaning that for every three vertices u, v, and w there is a unique median vertex m(u,v,w) that lies on shortest paths between ... As with median graphs more generally, squaregraphs are also partial cubes their vertices can be labeled with binary strings such that the Hamming ...
Graphs, Maps & Trees - Miscellanea
... "Graphs, Maps Trees" is the first single by Assembly Now to have an accompanying music video ...
Squaregraph - Characterization
... ways other than via their planar embeddings They are the median graphs that do not contain as an induced subgraph any member of an infinite family of ... These forbidden graphs are the cube (the simplex graph of K3), the Cartesian product of an edge and a claw K1,3 (the simplex graph of a claw), and the graphs formed from a gear graph by adding one more ... They are the graphs that are connected and bipartite, such that (if an arbitrary vertex r is picked as a root) every vertex has at most two neighbors closer to r, and such that at every vertex v, the ...
Crown Graph - Applications
... of n married couples, can be described as the Hamiltonian cycles of a crown graph ... the number of Hamiltonian cycles in a crown graph, is known in combinatorics as the ménage problem for crown graphs with 6, 8, 10.. ... sequence A094047 in OEIS) Crown graphs can be used to show that greedy coloring algorithms behave badly in the worst case if the vertices of a crown graph are presented to the algorithm in the order u0, v0 ...
Lévy Family Of Graphs
... In graph theory, a branch of mathematics, a Lévy family of graphs is a family of graphs Gn, n = 1, 2, 3.. ... Many naturally occurring families of graphs are Lévy families ... Formally, a family of graphs Gn, n = 1, 2, 3.. ...