Graph theory: Mail Route 1. Your friend is a mailman. He is given 3 possible rou

Question

Graph theory: Mail Route 1. Your friend is a mailman. He is given 3 possible route options. On each map he must start and end at the S e travel down each street at least one time. Which route should your friend choose? Why? Route 1 Route 2 Route 3 2. Which of the maps below have a route where the mailman can start and end at the same street corner (i.e. vertex) and travel down each street eractly once? (He can only travel on existing streets.) B D E C D C F Graph 2 Graph 3 Graph 1 Graph 4 Graph 5 Graph 6 more graphs on back

Explanation / Answer

(1) My friend chooses Route 1

because for Route 2 he can't travel down side and reach S , for Route 3 he can't end at S.

(2) Graph 1,Graph 4, Graph 6 maps have a route.

(3) In Graph 8 map i get stuck which doesn't have this special kind of route.

I get stucked in this location because it has overlap loop.

We start from vertices c and we end in veretices c twice,so it doesn't satisfy the rule.

(4) Graph 9 contains one of the special routes . In graph 9 first we have start from B and we can end with B by connecting (or) travelling down each street exactly once.

(4(b)) Graph 10 does not contains one of the special route. In graph 10 ,both the starting and ending vertices are not same. we travel down one or more streets more than once.

Therefore both conditions are not satisfied.

(5) Graph 9 map contains special route.

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