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Graph Theory
Let V={1,2,
,20} be the set of the first 20 positive integers. Consider the graphs whose vertex set is V and whose edge sets are defined below. For each graph, investigate whether the graph (i) is connected (if not connected, determine the connected components), (ii) is bipartite, (iii) has a Eulerian Trail, and (iv) has a Hamilton path.
a) {a,b} is an edge if and only if a+b is even.
b) {a,b} is an edge if and only if a*b is a perfect square.
c) {a,b} is an edge if and only if a-b is divisible by 3.
So. I think I could do it If I could get some help on HOW to do it? Maybe if someone can do 1 for me (there are 4 more not included here).
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