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A Mycielski graph M_k of order k is a triangle-free graph with chromatic number k having the smallest possible number of vertices. For example, triangle-free graphs with ...

A cubic semisymmetric graph is a graph that is both cubic (i.e., regular of degree 3) and semisymmetric (i.e., edge- but not vertex-transitive). The four smallest cubic ...

A quartic symmetric graph is a symmetric graph that is also quartic (i.e., regular of degree 4). The numbers of symmetric quartic graphs on n=1, 2, ... are 0, 0, 0, 0, 1, 1, ...

The truncated tetrahedral graph is the cubic Archimedean graph on 12 nodes and 18 edges that is the skeleton of the truncated tetrahedron. It is implemented in the Wolfram ...

The vertex height of a vertex v in a rooted tree is the number of edges on the longest downward path between v and a tree leaf. The height of the root vertex of a rooted tree ...

"The" octahedral graph is the 6-node 12-edge Platonic graph having the connectivity of the octahedron. It is isomorphic to the circulant graph Ci_6(1,2), the cocktail party ...

A zero-symmetric graph is a vertex-transitive cubic graph whose edges are partitioned into three orbits by its automorphism group. The figures above show some small ...

A graph corresponding to the skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, all of which are regular, planar, polyhedral, and Hamiltonian. The ...

The eccentricity epsilon(v) of a graph vertex v in a connected graph G is the maximum graph distance between v and any other vertex u of G. For a disconnected graph, all ...

A graph G that becomes disconnected when removing a suitable complete subgraph K, called a vertex cut, is said to be quasiseparable. The two simplest cases are those where K ...