GraphSum
GraphSum[g1,g2]
gives the graph sum of the graphs g1 and g2.
Details and Options

- GraphSum is also known as graph addition.
- GraphSum is typically used to produce multigraphs with particular subgraphs.
- GraphSum[g1,g2] gives a graph obtained by combining edges of the IndexGraph of g1 and g2.
- For graphs g1 and g2 having the same number of vertices, GraphSum[g1,g2] returns AdjacencyGraph[AdjacencyMatrix[g1]+AdjacencyMatrix[g2]].
- GraphSum takes the same options as Graph.

Examples
open allclose allScope (29)
Properties & Relations (5)
The sum of any graph and its complement is a CompleteGraph:
The sum of any graph and itself is a multigraph:
The sum of graphs can be obtained by joining the edges of the graphs:
The sum of graphs can be obtained by adding their adjacency matrices together:
GraphSum gives the same result as GraphUnion if graphs have different vertex names:
Neat Examples (1)
Text
Wolfram Research (2022), GraphSum, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphSum.html.
CMS
Wolfram Language. 2022. "GraphSum." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GraphSum.html.
APA
Wolfram Language. (2022). GraphSum. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GraphSum.html