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The Hoffman-Singleton graph is the graph on 50 nodes and 175 edges that is the only regular graph of vertex degree 7, diameter 2, and girth 5. It is the unique (7,5)-cage ...

The graph neighborhood of a vertex v in a graph is the set of all the vertices adjacent to v including v itself. More generally, the ith neighborhood of v is the set of all ...

The Dyck graph is unique cubic symmetric graph on 32 nodes, illustrated above in a number of embeddings. It is denoted F_(032)A in the Foster census of cubic symmetric graphs ...

The Knödel graph W_(Delta,n) is a regular bipartite graph of vertex degree Delta on n nodes for even n>=2 and 1<=Delta<=|_log_2n_| with edges defined as follows. Label the ...

Cubic symmetric graphs are sometimes called Foster graphs and denoted F_(nnn)X, where nnn is the vertex count and X is a letter A, B, C, ... indicating the particular such ...

The total graph T(G) of a graph G has a vertex for each edge and vertex of G and an edge in T(G) for every edge-edge, vertex-edge, and vertex-vertex adjacency in G ...

The small rhombicosidodecahedral graph is a quartic graph on 60 nodes and 120 edges that corresponds to the skeleton of the small rhombicosidodecahedron, as well as the great ...

The small rhombicuboctahedral graph is a quartic graph on 24 nodes and 48 edges that corresponds to the skeleton of the small rhombicuboctahedron. It has graph diameter 5, ...

The neighborhood graph of a given graph from a vertex v is the subgraph induced by the neighborhood of a graph from vertex v, most commonly including v itself. Such graphs ...

A (0,2)-graph is a connected graph such that any two vertices have 0 or 2 common neighbors. (0,2)-graphs are regular, and the numbers of (0,2)-graphs with vertex degree 0, 1, ...