Prove or disprove There exist at least two nonisomorphic gr

Prove or disprove : There exist at least two nonisomorphic graphs with degree sequence (1, 1, 1, 2, 2, 2, 2, 3)

Solution

writing degree sequence in descending order and using havell\'s hakibi theorem for degree sequence

3,2,2,2,2,1,1,1

=> 1,1,1,2,1,1,1

=> 0,1,2,1,1,1 this degree is false it can never occur in rea life

hence There cannot exist at least two nonisomorphic graphs with degree sequence (1, 1, 1, 2, 2, 2, 2, 3)