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A weighted graph in which the weights are equal to the Euclidean lengths of the edges in a specified embedding (Skiena 1990, pp. 201 and 252).

The co-rank of a graph G is defined as s(G)=m-n+c, where m is the number of edges of G, n is the number of vertices, and c is the number of connected components (Biggs 1993, ...

The rank of a graph G is defined as r(G)=n-c, where n is the number of vertices on G and c is the number of connected components (Biggs 1993, p. 25).

The union G=G_1 union 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 V=V_1 union V_2 and X=X_1 union X_2 (Harary ...

Given a function f(x_1,...,x_n) defined on a domain U, the graph of f is defined as the set of points (which often form a curve or surface) showing the values taken by f over ...

The nth-order Menger sponge graph is the connectivity graph of cubes in the nth iteration of the Menger sponge fractal. The first two iterations are shown above. The n-Menger ...

For an undirected graph, an unordered pair of nodes that specify a line joining these two nodes are said to form an edge. For a directed graph, the edge is an ordered pair of ...

The nth-order Sierpiński carpet graph is the connectivity graph of black squares in the nth iteration of the Sierpiński carpet fractal. The first three iterations are shown ...

The graph distance matrix, sometimes also called the all-pairs shortest path matrix, is the square matrix (d_(ij)) consisting of all graph distances from vertex v_i to vertex ...

The theorem, originally conjectured by Berge (1960, 1961), that a graph is perfect iff neither the graph nor its graph complement contains an odd graph cycle of length at ...