Intersection Operation
Let G1(V1,E1) and G2(V2,E2) be two graphs. Then the intersection of G1 and G2 is a graph G=G1∩G2, whose vertex set V=V1∩V2 and edge set E=E1∩E2.
For the above two graphs G1 and G2, we have vertices and edges as V1= { A, B, C, D, E } and E1= { 1,2,4,5,6,7 } and V2= {B, C, D, E, F} and E2= {3,5,7,8,9,10,11} respectively.
So, in order to find the intersection of graphs G1 and G2, which can be denoted as G= G1∩G2. The vertex set of graph G will be V=V1∩V2= {B, C, D, E} and the edge set of graph G will be E=E1∩E2 ={3,5,7}.
The resultant intersection graph G with all the vertices of set V and edges of set E will be as shown:
Be careful to retain the original order of vertices and edges as in the original graph in the resultant graph.
Union and Intersection Operation On Graph
In graph theory, the data/objects belong to the same group but each piece of data differs from one other. In this article, we will see union and intersection operations on the graph.