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The longhorn graph is the graph on 7 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["LonghornGraph"].

A connected graph is graph that is connected in the sense of a topological space, i.e., there is a path from any point to any other point in the graph. A graph that is not ...

The Johnson graph J(n,k) has vertices given by the k-subsets of {1,...,n}, with two vertices connected iff their intersection has size k-1. Special classes are summarized in ...

A graph for which the relations between pairs of vertices are symmetric, so that each edge has no directional character (as opposed to a directed graph). Unless otherwise ...

The gear graph, also sometimes known as a bipartite wheel graph (Brandstädt et al. 1987), is a wheel graph with a graph vertex added between each pair of adjacent graph ...

A section of a graph obtained by finding its intersection with a plane.

For a connected graph G of graph diameter d, the distance-k graph G_k for k=1, ..., d is a graph with the same vertex set and having edge set consisting of the pairs of ...

The double graph of a given graph G is constructed by making two copies of G (including the initial edge set of each) and adding edges u_1v_2 and v_1u_2 for every edge uv of ...

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 ...

An apex graph is a graph possessing at least one vertex whose removal results in a planar graph. The set of vertices whose removal results in a planar graph is known as the ...