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Let graph G have p points v_i and graph H have p points u_i, where p>=3. Then if for each i, the subgraphs G_i=G-v_i and H_i=H-u_i are isomorphic, then the graphs G and H are ...

A k-colored graph is a labeled k-colorable graph together with its coloring function (Finch 2003).

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 ...

The eigenvalues of a graph are defined as the eigenvalues of its adjacency matrix. The set of eigenvalues of a graph is called a graph spectrum. The largest eigenvalue ...

An integral embedding of a graph, not to be confused with an integral graph, is a graph drawn such that vertices are distinct points and all graph edges have integer lengths. ...

The moth graph is the 6-vertex graph illustrated above. It is implemented in the Wolfram Language as GraphData["MothGraph"].

A complete k-partite graph is a k-partite graph (i.e., a set of graph vertices decomposed into k disjoint sets such that no two graph vertices within the same set are ...

The cricket graph is the 5-vertex graph illustrated above. It is implemented in the Wolfram Language as GraphData["CricketGraph"].

The dart graph is the 5-vertex graph illustrated above. It is implemented in the Wolfram Language as GraphData["DartGraph"].

The R graph is the graph on 6 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["RGraph"].