Bounds on Second Hyper Zagreb Index for Four Graph Operations

Abstract

All praise and thanksgiving are due to Allah, the Most Gracious and Most Merciful, for His blessings and strength in finishing this thesis. It gives us great pleasure to extend our sincere gratitude to our supervisor, Dr. Maqsood Ahmad, for his energetic guidance and motivating demeanor, which made working on this project a breeze. Only with his leadership were my efforts successful. We would like to thank our institution and Dr. Muhammad Hussain, Head of the Mathematics Department, in particular for providing us with excellent research facilities that were necessary to achieve our objectives. We sincerely thank our cherished parents, relatives, and friends, as they have contributed much to our achievement.