Consider the following map of Middle Earth represented as a graph. Erebor Fornost Hobbiton Weathertop QBree ORivendell Moria O Tharbad Lorien O O Isengard OFangorn Lond Daer Dead Gap of Rohan Marshes Morannon Helm's Edoras O O Deep OFrech OBarad-dar o O Orodruin Edhellond Osgiliath Minas Morgul O Dol Amroth (a) Identify a vertex in the graph, which is: (i) Degree 1 (ii) Degree 2 (iii) Degree 3 (iv) Degree 4 (b) It's time for you to answer the age-old question: Can one simply walk into (and out of) Mordor? Specifically, if the hobbits leave from Hobbiton and travel to Orodruin, is it possible for them to return to Hobbiton without passing through any places they've already been? (i) What feature of a graph do you need to look for to determine this