Given two graphs G = [V ; E] and G0 = [V 0 ; E0 ],...

Given two graphs G = [V ; E] and G0 = [V 0 ; E0 ], and an isomorphism, f : V → V 0 , and making direct use of the formal definition for isomorphism:

(a) Explain why G and G0 must have the same number of vertices.

(b) Explain why G and G0 must have the same number of edges.

(c) Explain why G and G0 must have the same degree sequences.

(d) Given two vertices, u, v ∈ V explain why: u is connected to v → f(u) is connected to f(v)

Note: Problems that ask you to “explain” are asking for responses that can be less formal than problems that ask you to “prove”. Nonetheless, responses need to be sufficiently precise and based on definitions and theorems as given in the text. Explanations should be concise, but care must be taken to ensure that explanations are at an appropriate level of detail and will be clear to the intended reader.

Expert Solution

Doubts are welcome.

Thank You !

Colby Messinger answered 2 hours ago

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