Graph Intersection

Question

Answer 1

See the given 2 graphs are vertex disjoint since the labels used in the 2 graphs for vertices are different .Not a single vertex appears in both graph  G₁ and G₂ , since for G₁  ∩  G₂ , we require :

 V₁  ∩  V₂ for common vertices 

and E₁  ∩   E₂ for common edges but before that the vertices which are incident on that particular edge should also be common i both the graphs.

So according to the above graph , they are vertex disjoint and for vertex disjoint situation , even graphs do not exist at all but for edge disjoint situation , graph may exist. 

So the above is a vertex disjoint one.

Hence no of edges = no of vertices in G₁ ∩ G₂ = 0

Hence no of edges in G = 0

Comments

And then if it was both unlabbeled then their intersection would be the same graph..right??

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I dont think set operations are defined for unlabeled graphs.

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Yes u r right ..For set operations labels on the graph is necessary since we do set operations on edge set basically..So labelling must be done..Hence set operations are meaningless for undirected graph..