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Algorithmic graph theory is the study of graph traversal and generation and the complexity of these operations. Topics in algorithmic graph theory include Eulerian and ...

The set of graph eigenvalues of the adjacency matrix is called the spectrum of the graph. (But note that in physics, the eigenvalues of the Laplacian matrix of a graph are ...

A graph is planar if it can be drawn in a plane without graph edges crossing (i.e., it has graph crossing number 0). The number of planar graphs with n=1, 2, ... nodes are 1, ...

A traceable graph is a graph that possesses a Hamiltonian path. Hamiltonian graphs are therefore traceable, but the converse is not necessarily true. Graphs that are not ...

A septic graph is a regular graph of degree seven. The numbers of (not necessarily connected) simple septic graphs on n=8, 10, 12, ... vertices are 1, 5, 1547, 21609301, ...

A graph embedding, sometimes also called a graph drawing, is a particular drawing of a graph. Graph embeddings are most commonly drawn in the plane, but may also be ...

The (m,q)-Ustimenko graph is the distance-1 or distance-2 graph of the dual polar graph on [C_m(q)] (Brouwer et al. 1989, p. 279). The Ustimenko graph with parameters m and q ...

A graph G is said to be flexible if the vertices of G can be moved continuously so that (1) the distances between adjacent vertices are unchanged, and (2) at least two ...

The path graph P_n is a tree with two nodes of vertex degree 1, and the other n-2 nodes of vertex degree 2. A path graph is therefore a graph that can be drawn so that all of ...

A graph G is a hypotraceable graph if G has no Hamiltonian path (i.e., it is not a traceable graph), but G-v has a Hamiltonian path (i.e., is a traceable graph) for every v ...