Asian Journal of Mathematics and Computer Research

Topological indices provide numerical descriptors of graph structure and are widely used to relate molecular graph properties to structural features. This manuscript studies lower and upper bounds for selected degreebased topological indices of the Γ -graph, defined through the semi-total point graph of the vertex corona construction for two finite, simple and connected graphs G and H. Using an edge-partition approach, the work derives bounds in terms of the vertex and edge cardinalities of G and H, together with their minimum and maximum degrees. The indices considered are the first Zagreb index, the Nirmala index, the Sombor index, the hyper-Zagreb index, the Y -index and the V L-index. For each index, the corresponding formula is supported by illustrative computations on representative graph pairs, including paths, cycles and treetype graphs. These examples show that the computed index values lie within the stated lower and upper estimates, thereby demonstrating the consistency of the proposed bounding framework for the selected cases. The presentation also clarifies how the degree contributions from different edge classes determine the final expressions. The study contributes a structured treatment of Γ-graph bounds for several commonly used degree-based descriptors and indicates how the same edge-decomposition method may be adapted to related graph invariants, subject to careful verification of the underlying graph parameters.