Union and intersection of graphs

A graph union is an operation on graphs that results in a graph whose vertex sets and edges are unions of vertex sets and edges of the original graphs. In other words, the resulting graph includes all edges and vertices that are present in the original graphs ^[1] .

The operation of combining graphs, as well as a similar operation for sets, is usually denoted by the symbol :

So, if

that

Where - many vertices, - set of edges of the graph.

The intersection of graphs is an operation on graphs, as a result of which a graph is obtained whose vertex sets and edges are intersections of the sets of vertices and edges of the original graphs. In other words, the resulting graph includes only those edges and those vertices that are present in all the original graphs ^[1] .

The operation of intersection of graphs, as well as a similar operation for sets, is usually denoted by the symbol :

So, if

that

Where - many vertices, - many edges of the graph.