Write mathematical report with mathetmatical notation that includes these $4$ paragraphs $($Defintion$,$ objective, solution, Explanation$)$: The tournament structure needs to be set; that is to say, who plays who. For this tournament a

structure is used where all games are set at the beginning. Another committee member will propose

the tournament structure and your job is to determine whether it has the required properties. The

committee has determined that the following properties are sufficient:

$$ For every pair of distinct players, either they play against each other, or there are at least two

other players that they both play against.

$$ All players have the same number of games.

So for example, if Alice and Bob don$$t play against each other then it$$s still OK as long as they both

play against two players in common, say, Charlie and Denise.

Your job is to find a method that, given a tournament structure, determines whether the above propterties hold.