Extremal Values on the General Degree–Eccentricity Index of Unicyclic Graphs of Fixed Diameter

For a connected graph G and two real numbers a, b, the general degree–eccentricity index of G is given by DEIa,bG=∑v∈VGdGavecGbv, where V(G) represent the vertex set of graph G, dG(v) denotes the degree of vertex v, and ecG(v) is the eccentricity of v in G, that is, the maximum distance from v to another vertex of G. This index generalizes several well‐known “topological indices” of graphs such as the eccentric connectivity index. We characterize the unique unicyclic graph with the maximum general degree–eccentricity index for the case a ≥ 1, b ≤ 0 and the minimum general degree–eccentricity index for the case 0 ≤ a ≤ 1, b ≥ 0, among all n‐vertex unicyclic graphs with fixed order and diameter.