Faisal Abdul-Karim Fairag2022-05-182022-05-185440https://drepo.sdl.edu.sa/handle/20.500.14154/2195The eigenvalues of a graph are the eigenvalues of its adjacency matrix. Let ?1and ?2 denote the largest and the second largest eigenvalue, respectively. The family of trees having only three end vertices and satisfying a certain equality involving ?1and ?2 is characterized. Also, bounds on ?2 for the above family of trees are investigated.enThesis