Mesfin MasreHana Adugna2025-09-122025-09-122024-08https://etd.aau.edu.et/handle/123456789/7440The general eccentric connectivity index of graphs is the main topic of this study. For a connected graph G, the general eccentric connectivity index of graph G is defined by ECIa(G) = Σ v∈V(G) eccG(v)daG (v) for a ∈ R, where the degree of v in G is dG(v), the eccentricity of vertex v is eccG(v), and the vertex set of G is V(G). In this thesis, we study the general degree-eccentricity index of graphs. Among all the unicyclic graphs of a particular order and matching number, we identify the unicyclic graphs with the largest and smallest general eccentric connectivity index.en-USGeneral EccentricConnectivity IndexGraphsThesis