Extremal graphs with given parameters in respect of general ABS index

For a graph. = (.,.), the general atom-bond sum-connectivity index is formulated by........(.) = S...... (.)(.... +.... -2.... +....).., where.... indicates the degree of vertex....,.. can be arbitrary real number. Several physicochemical features of benzenoid hydrocarbons can be correctly anticipated using the........ index. Researchers go through careful inspection of some........ and reveal that......1,...... -1,...... 12,...... 3 enjoy benefit in foreseeing the boiling point, the standard enthalpy of vaporization, the acentric factor, and the entropy of octane isomers, separately. One significant wellspring of information for exploring the molecular construction is the assessed worth of the reach for topological indices through certain predefined molecular graph parameters. The purpose of the present work is to find the highest values of the........ index for.. = 0 in the set of graphs that were given certain predefined parameters, such as matching number, chromatic number, etc. Furthermore, illustrations of the relevant extremal graphs were provided.