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( 3 ) ( i ) If a graph with 7 vertices has degrees 6 , 6 , 4 , 3 , 3 , 3
i If a graph with vertices has degrees what is the smallest value that could have? Draw an example of a graph for which takes this value.
ii What is the least possible number of edges in a connected graph with vertices in which each edge is in at least two cycles? Draw an example of such a graph with this number of edges.
iii Let be an even integer. What is the greatest possible number of edges in a graph with vertices in which each vertex has even degree? Give your answer as an expression in terms of For draw an example of such a graph with this number of edges.
Answers only required this includes a picture for each part
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