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A loop of an graph is degenerate edge that joins a vertex to itself, also called a self-loop. A simple graph cannot contain any loops, but a pseudograph can contain both ...

The Dejter graph is a weakly regular graph on 112 vertices and 336 edges with regular paremeters (nu,k,lambda,mu)=(112,6,0,(0,1,2)). It can be obtained by deleting a copy of ...

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

A graph in which individual nodes have no distinct identifications except through their interconnectivity. Graphs in which labels (which are most commonly numbers) are ...

The thickness (or depth) t(G) (Skiena 1990, p. 251; Beineke 1997) or theta(G) (Harary 1994, p. 120) of a graph G is the minimum number of planar edge-induced subgraphs P_i of ...

A graph H is a minor of a graph G if a copy of H can be obtained from G via repeated edge deletion and/or edge contraction. The Kuratowski reduction theorem states that any ...

A connected graph G is distance-regular if for any vertices x and y of G and any integers i,j=0, 1, ...d (where d is the graph diameter), the number of vertices at distance i ...

The Sierpiński gasket graph of order n is the graph obtained from the connectivity of the Sierpiński sieve. The first few Sierpiński gasket graphs are illustrated above. S_2 ...

A bridged graph is a graph that contains one or more graph bridges. Examples of bridged graphs include path graphs, ladder rung graphs, the bull graph, star graphs, and ...

The word "rigid" has two different meaning when applied to a graph. Firstly, a rigid graph may refer to a graph having a graph automorphism group containing a single element. ...