If 10 people each shake hands with each other, how many handshakes took place? W

Question

If 10 people each shake hands with each other, how many handshakes took place? What does this question have to do with graph theory? Among a group of 5 people, is it possible for everyone to be friends with exactly 2 of the people in the group? What about 3 of the people in the group? Is it possible for two different (non-isomorphic) graphs to have the same number of vertices and the same number of edges? What if the degrees of the vertices in the two graphs are the same (so both graphs have vertices with degrees 1, 2, 2, 3, and 4, for example)? Draw two such graphs or explain why not. Are the two graphs below equal? Are they isomorphic? If they are isomorphic, give the isomorphism. If not, explain. Graph 1: V = {a, b, c, d, e}. E = {{a, b}, {a, c}, {a, e}, {b, d}, {b, e}, {c, e}}. Graph 2:

Explanation / Answer

As per chegg's guideline i am bound to answer the first question only so kindly rate according to this rule.

Given below is the answer to Question 1.

The first person shakes everyone's hand. Thus there are 9 handshakes, as he/she doesn't shake his/her own hand.

The second person already shook the first person's hand, thus he/she shakes only 8 other hands.

Simlilary rest of the person follows the same thing and hence we arrive at the following solution :-

9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45.

Therefore, there are 45 handshakes.

You can think of this whole scenerio in graph theory as following :-

G have 10 vertices with degree 9 . So total degree is 10 * 9 = 90

We know that degree = 2* ( no. of edges)

Here , No. of edges represents handshakes.

So no. of handshakes = no . of edges = 90/2 =45

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