The properties of chemical compounds are very important for the studies of the non-isomorphism phenomenon's related to the molecular graphs. Topological indices (TIs) are one of the mathematical tools which are used to study these properties. Gutman and Trinajsti [Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons. Chem Phys Lett. 1972;17(4):535–538] defined the Zagreb indices (descriptors) to find correlation value between a molecular graph and its total π-electron energy. Later on, Bollobás and Erdös [Graphs of extremal weights. Ars Comb; 1998;50:225–233] defined the most general form of these indices (descriptors) called by general Randić index (GRI) and first general Zagreb index (FGZI), respectively. In this paper, we computed the bounds for FGZI and GRI of φ-sum graphs, obtained by the strong product of the graph $\phi \left(G\right)$ with another graph Γ, where $\phi \left(G\right)$ is constructed using four subdivision operations on the graph G. At the end, we also include the results for some particular families of graphs as the applications of the obtained results.

化合物的性质对于研究与分子图有关的非同构现象非常重要。拓扑指数（TIs）是用于研究这些属性的数学工具之一。Gutman和Trinajsti [图论和分子轨道。交替碳氢化合物的总π电子能。化学物理通讯。1972; 17（4）：535–538]定义了Zagreb指数（描述符）以查找分子图与其总π之间的相关值-电子能量。后来，Bollobás和Erdös[极重图。Ars Comb；1998; 50：225–233]定义了这些索引（描述符）的最一般形式，分别由一般Randić指数（GRI）和第一个一般Zagreb指数（FGZI）调用。在本文中，我们计算了φ- sum图的FGZI和GRI的界限，该界限是通过该图的强积获得的$\phi （G）$ 与另一个图Γ， $\phi （G）$使用图G上的四个细分运算构造。最后，我们还将某些特定图族的结果作为所得结果的应用。