Q1) how many graphs are there on 20 nodes? (To make this question precise, we have to make sure we known what it mean that two graphs are the same . For the purpose of this exercise,we consider the nodes given and labeled,say,asAlice ,Bob,...... The graph consisting of a single edge connecting Alice and Bob is different from the graph consisting of a single edge connecting Eve and frank.)

Q2) Formulate the following assertion as a theorem about graphs and prove it :At every party one can find two people who know

the same number of other people (like Bob and Eve in our first example).