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 , where V ( G ) represent the vertex set of graph G , d G ( v ) denotes the degree of vertex v , and e c G ( 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.