Extremal Euler Sombor Index of Unicyclic Graphs with Fixed Diameter

Topological indices are numerical descriptors of graphs that are widely used in fields such as mathematical chemistry, network theory, and structural analysis.Among the recently introduced degreebased indices, the Euler Sombor index has gained significant attention due to its applicability.The Euler Sombor index is defined as:where dG(x) denotes the degree of vertex x in the graph G, and the sum is taken over all edges of G.In this study, we focus on the minimum value of the Euler Sombor index for the class of unicyclic graphs with a fixed diameter d 2.