The join 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 union G_1 union G_2 together with all the edges joining V_1 and V_2. Graph joins are implemented in the Wolfram Language as GraphJoin[G1, G2]. A complete k-partite graph K_(i, j, ...) is the graph join of empty graphs on i, j, ... nodes. A wheel graph is the join of a cycle graph and the singleton graph. Finally, a star graph is the join of an empty graph and the singleton graph.

cone graph | dipyramidal graph | fan graph | graph Cartesian product | graph sum | graph union | star graph | wheel graph | windmill graph