Question: Use the theorems on graphs and trees to help you with this question. (a) Either draw a tree with 5 vertices and total degree

Use the theorems on graphs and trees to help you with this

Use the theorems on graphs and trees to help you with this question. (a) Either draw a tree with 5 vertices and total degree 10, or explain why no such graph exists. (b) Either draw a connected graph that has a circuit, 7 vertices, and 6 edges; or explain why no such graph exists. (c) Either draw a graph that is circuit-free, has 7 vertices, and 4 edges; or explain why no such graph exists. (d) A connected graph has 11 vertices and 10 edges. Does it have a vertex of degree 1? 1

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