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A portion of a disk whose upper boundary is a (circular) arc and whose lower boundary is a chord making a central angle theta<pi radians (180 degrees), illustrated above as ...

The complete bipartite graph K_(1,3) is a tree known as the "claw." It is isomorphic to the star graph S_4, and is sometimes known as the Y graph (Horton and Bouwer 1991; ...

Curves which, when rotated in a square, make contact with all four sides. Such curves are sometimes also known as rollers. The "width" of a closed convex curve is defined as ...

A snark on 30 vertices with edge chromatic number 4. It is implemented in the Wolfram Language as GraphData["DoubleStarSnark"].

A geometry in which Euclid's fifth postulate holds, sometimes also called parabolic geometry. Two-dimensional Euclidean geometry is called plane geometry, and ...

The Foster cage is one of the four (5,5)-cage graphs. Like the other (5,5)-cages, the Foster cage has 30 nodes. It has 75 edges, diameter 3, girth 5, chromatic number 4, and ...

The Franklin graph is the 12-vertex cubic graph shown above whose embedding on the Klein bottle divides it into regions having a minimal coloring using six colors, thus ...

The centroid is center of mass of a two-dimensional planar lamina or a three-dimensional solid. The mass of a lamina with surface density function sigma(x,y) is ...

The great rhombicosidodecahedral graph is the Archimedean graph on 120 vertices and 180 edges that is the skeleton of the great rhombicosidodecahedron as well as the uniform ...

Grünbaum conjectured that for every m>1, n>2, there exists an m-regular, m-chromatic graph of girth at least n. This result is trivial for n=2 and m=2,3, but only a small ...