Identical Graphs¶
Identical Graphs¶
Consider graphs G and H. Graphs G and H are said to be identical if V(G) = V(H) and E(G) = E(H).
Isomorphism¶
Consider graphs G and H. Let's define a bijective function f from V(G) to V(H), where f(u) is the corresponding vertex in graph H for vertex u in graph G, with the condition that f(u) and f(v) are equal if and only if u is equal to v. If a function f can be created between the vertices of G and H such that by mapping each vertex u in graph G to f(u), the two graphs become identical (i.e., the structure of G under f perfectly matches H), then these two graphs are called isomorphic. In other words, an edge uv exists in G if and only if an edge f(u)f(v) also exists in H; in this case, the two graphs are isomorphic.
Automorphism¶
The simple definition of automorphism is an isomorphism of a graph to itself. Meaning, by permuting the vertices of the graph, the set of edges does not change.
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