If two graphs G and H contain the same number of vertices connected in the same way, they are called isomorphic graphs (denoted by G ≅ H).
It is easier to check non-isomorphism than isomorphism. If any of these following conditions occurs, then two graphs are non-isomorphic −
The following graphs are isomorphic −
A homomorphism from a graph G to a graph H is a mapping (May not be a bijective mapping) h: G → H such that − (x, y) ∈ E(G) → (h(x), h(y)) ∈ E(H). It maps adjacent vertices of graph G to the adjacent vertices of the graph H.
A homomorphism is an isomorphism if it is a bijective mapping.
Homomorphism always preserves edges and connectedness of a graph.
The compositions of homomorphisms are also homomorphisms.
To find out if there exists any homomorphic graph of another graph is a NPcomplete problem.