Molecular descriptors are essential in mathematical chemistry for studying quantitative structure-property relationships (QSPR), and topological indices are a valuable source of information about molecular properties such as size, cyclicity, branching degree, and symmetry. Graph theory has played a crucial role in the development of topological indices and dominating parameters for molecular descriptors. The molecule graph, under graph isomorphism conditions, represents an invariant number, and the graph theory approach considers dominating sets, which are subsets of the vertex set where every vertex outside the set is adjacent to at least one vertex inside the set. The dominating sigma index, a topological index that incorporates the mathematical principles of domination topological indices and the sigma index, is applicable to some families of graphs, such as book graphs, windmill graphs, and some graph operations, which have exact values for this new index. To evaluate the effectiveness of the domination sigma index in QSPR studies, a comparative analysis was conducted to establish an appropriate domination index that correlates with the physicochemical properties of octane and its isomers. Linear and non-linear models were developed using the QSPR approach to predict the properties of interest, and the results showed that both the domination forgotten and domination first Zagreb indices exhibited satisfactory performance in comparison testing. Further research into QSAR/QSPR domination indices is required to build more robust models for predicting the physicochemical properties of organic compounds while maintaining the importance of symmetry.

Topological indices have important role in theoretical chemistry for QSPR researches. Among the all topological indices the Randić and the Zagreb indices have been used more considerably than any other topological indices in chemical and mathematical literature. Most of the topological indices as in the Randić and the Zagreb indices are based on the degrees of the vertices of a connected graph. Recently novel two degree concepts have been defined in graph theory; ev-degrees and ve-degrees. In this study we define ev-degree Zagreb index, ve-degree Zagreb indices and ve-degree Randić index by using these new graph invariants as parallel to their corresponding classical degree versions. We compare these new group ev-degree and ve-degree indices with the other well-known and most used topological indices in literature such as; Wiener, Zagreb and Randić indices by modelling some physicochemical properties of octane isomers. We show that the ev-degree Zagreb index, the ve-degree Zagreb and the ve-degree Randić indices give better correlation than Wiener, Zagreb and Randić indices to predict the some specific physicochemical properties of octanes. We investigate the relations between the second Zagreb index and ev-degree and ve-degree Zagreb indices and some mathematical properties of ev-degree and ve-degree Zagreb indices.

Experimental studies and numerical analyses were conducted to estimate the laminar flame speeds of butyl ether, n-octane, iso-octane, and 1-octene at temperatures of 373 and 443 K and pressures ranging from 0.03 to 0.3 MPa in a constant-volume combustion chamber. Iso-octane had the slowest laminar flame speed whereas butyl ether had the highest. The LLNL model for large hydrocarbons and the Cai model for butyl ether were combined to describe the chemical kinetic mechanism for the test fuels. The simulation data calculated with the constructed model agree with the experimental data. The discrepancies in the laminar flame speeds of the four fuels were clarified from the perspectives of thermodynamics, diffusion, and chemical kinetics. The results reveal that the thermodynamics and chemical kinetics were dominant. Butyl ether had the highest laminar flame speed. This was attributed to it having the highest adiabatic flame temperature and a higher concentration of H and OH radicals, which have a high reactivity in a flame. Iso-octane produces the highest concentration of CH3, which inhibits flame propagation, so that it had the slowest laminar flame speed.