Graph shape names4/22/2024 ![]() When you think of a cycle in everyday life, you probably think of something that begins and ends the same way. (credit: "Diagram of the water cycle" by NASA, Public Domain) So, the total number of introductions is n ( n − 1 ) 2 n ( n − 1 ) 2.įigure 12.29 The water cycle begins and ends with water. By the Sum of Degrees Theorem, the number of edges is half the sum of the degrees, which is n ( n − 1 ) 2 n ( n − 1 ) 2. Since there are n n vertices of degree n − 1 n − 1, the sum of degrees is n ( n − 1 ) n ( n − 1 ). Since each individual must meet n − 1 n − 1 other individuals, there are n − 1 n − 1 edges meeting at each vertex which means each vertex has degree n − 1 n − 1. Since there are n n strangers, there are n n vertices.So, the total number of introductions is 45. By the Sum of Degrees Theorem, the number of edges is half the sum of the degrees, which is 90 2 = 45 90 2 = 45. Since there are 10 vertices of degree 9, the sum of degrees is 10 ⋅ 9 = 90 10 ⋅ 9 = 90. Since each individual must meet 9 other individuals, there are 9 edges meeting at each vertex which means each vertex has degree 9. Since there are 10 strangers, there are 10 vertices.So, the total number of introductions is 15. By the Sum of Degrees Theorem, the number of edges is half the sum of the degrees, which is 30 2 = 15 30 2 = 15. Since there are 6 vertices of degree 5, the sum of degrees is 6 ⋅ 5 = 30 6 ⋅ 5 = 30. ![]() ![]() Since each individual must meet 5 other individuals, there are 5 edges meeting at each vertex which means each vertex has degree 5. Since there are 6 strangers, there are 6 vertices.Use the Sum of Degrees Theorem to determine the number of introductions required in a room with
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