GraphJoin
GraphJoin[g1,g2]
gives the graph join of the graphs g1 and g2.
Details and Options

- GraphJoin is also known as complete union.
- GraphJoin is typically used to produce new graphs with particular reachable subgraphs.
- GraphJoin[g1,g2] gives a graph obtained from g1 and g2 by joining each vertex of g1 to all vertices of g2.
- GraphJoin[g1,g2] returns GraphDisjointUnion[g1,g2] together with all edges between each vertex of IndexGraph[g1] and each vertex of IndexGraph[g2,n+1], where n is the VertexCount for g1.
- GraphJoin takes the same options as Graph.

Examples
open allclose allBasic Examples (3)
Scope (29)
Properties & Relations (4)
Joining the adjacency matrix of two graphs on diagonal and others are ones gets the adjacency matrix of GraphJoin:
The join of a single vertex to an empty graph gets a star graph:
The join of a single vertex to a cycle graph
gets a wheel graph
:
The join of empty graphs on ,
, ... nodes gets a complete
-partite graph
:
Text
Wolfram Research (2022), GraphJoin, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphJoin.html.
CMS
Wolfram Language. 2022. "GraphJoin." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GraphJoin.html.
APA
Wolfram Language. (2022). GraphJoin. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GraphJoin.html