Gutman Connection Index of Graphs under Operations

In the modern era, mathematical modeling consisting of graph theoretic parameters or invariants applied to solve problems existing in various disciplines physical sciences like computer sciences, physics, and chemistry. Topological indices (TIs) are one which frequently used identify different physicochemical structural properties molecular graphs. Wiener index is first distance-based TI that compute boiling points paraffine. For a F, recently developed Gutman Connection (GC) defined on all unordered pairs vertices as sum multiplications connection numbers distance between them. this note, GC operation-based symmetric networks called by derived D1(F) (subdivision graph), second D2(F) (vertex-semitotal third D3(F) (edge-semitotal graph) fourth D4(F) (total computed their general expressions TIs parent where these graphs obtained applying operations subdivision, vertex semitotal, edge semitotal total F respectively.