Reza Sharafdini

In this thesis, we study some eccentric-based topological indices as connective eccentricity index (CEI), augmented eccentric connectivity (AECI) and eccentric adjacency index (EAI). We investigate the maximal and the minimal values of these indices among all n-vertex graphs with fixed number of pendent vertices and characterize the extremal graphs. In addition, we study the cactus on n vertices with k cycles having the maximal connective eccentricity index. We also, we make a algebraic approach to this indices. To do so, first we compute these indices for various graphs using the group of automorphisms ofG. This is an efficient method of finding these indices especially when the automorphism group ofG has a few orbits on V (G ) or E (G ). Second we associate a matrix to each index and we investigate spectral property of this matrices. Then we study the energy of syhis matrices.