"Graph" means "simple graph" unless specified

(3) (a) What is the greatest possible number of edges in graph with 5 vertices that does not contain any cycles of length 5 ? Draw an example of such a graph with this number of edges. (b) What is the least possible number of edges in a connected graph with 8 vertices that contains a complete graph of order 5 as a subgraph and does not contain any bridges? Draw an example of such a graph with this number of edges. (c) Let n be an integer such that n4. What is the least possible number of edges in graph with n vertices in which each edge is in at least two different cycles? Give your answer as an expression in terms of n. [Give a number and a picture for (a) and (b). Give an expression for (c).] (3) (a) What is the greatest possible number of edges in graph with 5 vertices that does not contain any cycles of length 5 ? Draw an example of such a graph with this number of edges. (b) What is the least possible number of edges in a connected graph with 8 vertices that contains a complete graph of order 5 as a subgraph and does not contain any bridges? Draw an example of such a graph with this number of edges. (c) Let n be an integer such that n4. What is the least possible number of edges in graph with n vertices in which each edge is in at least two different cycles? Give your answer as an expression in terms of n. [Give a number and a picture for (a) and (b). Give an expression for (c).]