What are graphs?

Some articles on graphs, graph:

Squaregraph - Characterization
... several 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 forbidden graphs ... 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 vertex ... 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 ...
Squaregraph - Related Graph Classes
... The squaregraphs 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 ... As with median graphs more generally, squaregraphs are also partial cubes their vertices can be labeled with binary strings such that the Hamming distance between strings is equal to the shortest ...
Crown Graph - Applications
... of n married couples, can be described as the Hamiltonian cycles of a crown graph ... or almost equivalently 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 ...
Graphs, Maps & Trees - Miscellanea
... "Graphs, Maps Trees" is the first single by Assembly Now to have an accompanying music video ...