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Chapter 1
Chapter 2 (except 2-1)
Chapter 3
Chapter 4 (except 4-7 and 4-8)
Chapter 8
Chapter 9
Chapter 11 (all algorithms except Isomorphism and Planarity testing)

Note : This is according to 2018 Gate syllabus, might change for successive years.

EDIT : syllabus isn't changed from 2018 so you can follow the above.
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Where can I find solutions to Narsingh Deo Book for Graph theory any online links and pdf will be helpful ?