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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) ...

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

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 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 ...

A 1-factor of a graph G with n graph vertices is a set of n/2 separate graph edges which collectively contain all n of the graph vertices of G among their endpoints.

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 number of nodes in a graph is called its order.

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).

Das (2018) defines the triameter of a connected graph G with vertex set V and vertex count at least 3 as tr(G)=max{d(u,v)+d(v,w)+d(u,w):u,v,w in V}, where d(i,j) is the graph ...

Assignment of each graph edge of a graph to one of two color classes (commonly designation "red" and "green").