Mesfin MasreHelen Tizazu2025-09-052025-09-052024-08https://etd.aau.edu.et/handle/123456789/7359In this thesis, we introduce the general eccentric connectivity coindex, ECCIa of connected graphs. For a connected graph G order n, we define the general eccentric connectivity coindex as ECCIa(G) = Σ v∈V(G) ecca G[n−1−dG(v)] for a ∈ R, where E(G) is the edge set of graph G , dG(v) is the degree of vertex v and V(G) is the vertex set of graph G. We study, the general eccentric connectivity coindex of tree graphs of a given graph parameters. We determine trees with the maximum and minimum general eccentric connectivity coindex among all trees of a given graph parameters for a > 1.en-USGeneral EccentricConnectivity CoindexGraphsThesis