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A biconnected graph is a connected graph having no articulation vertices (Skiena 1990, p. 175). An equivalent definition for graphs on more than two vertices is a graph G ...

A binary tree is a tree-like structure that is rooted and in which each vertex has at most two children and each child of a vertex is designated as its left or right child ...

The cuboctahedral graph is an Archimedean quartic symmetric graph on 12 nodes and 24 edges that is the skeleton of the cuboctahedron, as well as the uniform ...

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

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 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 ...

The Robertson-Wegner graph is of the four (5,5)-cage graphs, also called Robertson's cage (Read and Wilson 1998, p. 273). Like the other (5,5)-cages, the Robertson-Wegner ...

The Robertson graph is the unique (4,5)-cage graph, illustrated above. It has 19 vertices and 38 edges. It has girth 5, diameter 3, chromatic number 3, and is a quartic ...