Discrete mathematics Class 1100 Graph Theory Please explain

10. Give an example of a graph with degree sequence 5,2,1,1,1, or show that such a graph cannot exist.

Solution

Answer :No such graph exists!

Explanation: In a graph with n-vertices , any vertex can have a maximum degree of n-1, since each vertex is left with only n-1 other vertices to connect(be adjacent) to.Hence for a 5 vertex graph , as is the case here, a degree sequence of 5 is not possible.

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