GraphJoin - Maple Help

GraphTheory

 GraphJoin
 construct join of graphs

 Calling Sequence GraphJoin(G, H)

Parameters

 G, H - graphs

Description

 • The GraphJoin(G,H) function returns the graph which is obtained by connecting all the vertices of G to all vertices of H. The vertex labels in the resulting graph are strings of the form "1:u" and "2:v" where u is a vertex in G and v is a vertex in H.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $G≔\mathrm{GraphJoin}\left(\mathrm{PathGraph}\left(2\right),\mathrm{Graph}\left(3\right)\right)$
 ${G}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 5 vertices and 7 edge\left(s\right)}}$ (1)
 > $\mathrm{Vertices}\left(G\right)$
 $\left[{"1:1"}{,}{"1:2"}{,}{"2:1"}{,}{"2:2"}{,}{"2:3"}\right]$ (2)
 > $\mathrm{Edges}\left(G\right)$
 $\left\{\left\{{"1:1"}{,}{"1:2"}\right\}{,}\left\{{"1:1"}{,}{"2:1"}\right\}{,}\left\{{"1:1"}{,}{"2:2"}\right\}{,}\left\{{"1:1"}{,}{"2:3"}\right\}{,}\left\{{"1:2"}{,}{"2:1"}\right\}{,}\left\{{"1:2"}{,}{"2:2"}\right\}{,}\left\{{"1:2"}{,}{"2:3"}\right\}\right\}$ (3)