Question

suppose Alice, Bob, Carol Dave and Eden attend a party. Alice shakes hand with Bob, Carol and Eden; Bob shakes hand with Alice and Dave; Carol shakes hand with Alice and Dave; Dave shakes hand with Bob and Carol; Eden shakes hand with Alice

1) represent the above scenario as a graph and define your notation is this graph cyclic or acyclic, directed or undirected?

2) find the degrees of each vertex in your graph are there two vertexes that have same degree? what does this mean in actual?

3) someone claims that if n people attend a party and some shake hands with others ( but not with themselves), then at the end, there will always be at least two people who have shaken hands with the same number of people

is that true or false?

4)suppose n people attend a party, what are the possible number of people that a person can shake hand with?

5)prove your result in (3)

Answer 1