Use the theorems on graphs and trees to help you with this question. (a) Either draw...

 

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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 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