In Exercises 60 and 61, you are scheduling a dinner party for six people (A, B, C, D, E, and F). The guests are to be seated around a circular table, and you want to arrange the seating so that each guest is seated between two friends (i.e., the guests to the left and to the right are friends of the guest in between). You can assume that all friendships are mutual (when X is a friend of Y, Y is also a friend of X).
Suppose that you are told that all possible friendships canbe deduced from the following information:A is friends with B and F; B is friends with A, C, and E; C isfriends with B, D, E, and F; E is friends with B, C, D, and F.
(a) Draw a “friendship graph” for the dinner guests.
(b) Find a possible seating arrangement for the party.
(c) Is there a possible seating arrangement in which B andE are seated next to each other? If there is, find it. Ifthere isn’t, explain why not.
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