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The composition G=G_1[G_2] of graphs G_1 and G_2 with disjoint point sets V_1 and V_2 and edge sets X_1 and X_2 is the graph with point vertex V_1×V_2 and u=(u_1,u_2) ...

Given a "good" graph G (i.e., one for which all intersecting graph edges intersect in a single point and arise from four distinct graph vertices), the crossing number is the ...

The cube of a graph is defined as its third graph power.

A cycle of a graph G, also called a circuit if the first vertex is not specified, is a subset of the edge set of G that forms a path such that the first node of the path ...

The graph diameter of a graph is the length max_(u,v)d(u,v) of the "longest shortest path" (i.e., the longest graph geodesic) between any two graph vertices (u,v), where ...

The graph difference of graphs G and H is the graph with adjacency matrix given by the difference of adjacency matrices of G and H. A graph difference is defined when the ...

Let the vertices of a graph G be numbered with distinct integers 1 to |G|. Then the dilation of G is the maximum (absolute) difference between integers assigned to adjacent ...

The dimension e(G), also called the Euclidean dimension (e.g., Buckley and Harary 1988) of a graph, is the smallest dimension n of Euclidean n-space in which G can be ...

A graph cycle.

The distance d(u,v) between two vertices u and v of a finite graph is the minimum length of the paths connecting them (i.e., the length of a graph geodesic). If no such path ...