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if G and G* are isomorphic graphs , then no of connected components of G* if G has connected components, are

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Vertex are also known as "nodes"

Edges are also known as "links"

For two graphs to be isomorphic (same) they must have the following properties:

  • The same number of vertices
  • The same number of edges  
  • The same degrees for corresponding vertices  
  • The same number of connected components
  • The same number of loops.
  • The same number of parallel edges.
  •  Both graphs are connected or both graphs are not connected,
  •  Pairs of connected vertices must have the corresponding pair of vertices connected.

Example of Isomorphic graphs:

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