Browsing by Author "Hana Adugna"

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    On the General Eccentric Connectivity Index of Graphs
    (Addis Ababa University, 2024-08) Hana Adugna; Mesfin Masre
    The 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.