Discrete math on multipartite graph. 1.The complete Multi-partite graph K_{n_{1}, n_{2}, n_{3}, n_{4}, ..., n_{m}}

sdentatoiz

sdentatoiz

Answered question

2022-09-04

Discrete math on multipartite graph
1.The complete Multi-partite graph
K n 1 , n 2 , n 3 , n 4 , . . . , n m
2.the number of edge of
K n 1 , n 2 , n 3 , n 4 , . . . , n m

Answer & Explanation

Medwsa1c

Medwsa1c

Beginner2022-09-05Added 17 answers

Step 1
Each vertex in n i has degree j = 1 , j i n | n j | , as each vertex in n i is incident to every vertex in the other partitions. There are | n i | vertices in n i , so that's why we multiply out.
Step 2
So by the handshake lemma, we get:
i = 1 n ( | n i | j = 1 , j i n | n j | ) = 2 E

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