2. (Graph Theory) An undirected simple graph with n vertices is regular if each vertex has the same degree, i.e., the same number of incident edges. A regular graph is said to be d-regular if each vertex has degree d. (1) Draw a 2-regular graph of 4 vertices. (2) Draw a 3-regular graph of 4 vertices. (3) Someone claims that if a d-regular graph of n vertices exists, then n2d+1. Is this claim correct? Explain why? (Note that a d-regular graph is a simple graph.) (4) Someone claims that if a d-regular graph of n vertices exits, then nd must be even. Is this claim correct? Explain why? 2. (Graph Theory) An undirected simple graph with n vertices is regular if each vertex has the same degree, i.e., the same number of incident edges. A regular graph is said to be d-regular if each vertex has degree d. (1) Draw a 2-regular graph of 4 vertices. (2) Draw a 3-regular graph of 4 vertices. (3) Someone claims that if a d-regular graph of n vertices exists, then n2d+1. Is this claim correct? Explain why? (Note that a d-regular graph is a simple graph.) (4) Someone claims that if a d-regular graph of n vertices exits, then nd must be even. Is this claim correct? Explain why