Abstract
Counting Polynomial is the mathematical function that was initially introduced for application in chemistry in 1936 by G. Polya. Partitioning of graphs can be seen in the coefficients of these mathematical functions, which also reveal the frequency with which these partitions happen. We developed a novel and efficient method for constructing the necessary counting polynomials for a zigzag-edge coronoid formed by the fusion of a Starphene graph and a Kekulenes graph. The study's methods expand our knowledge, and its findings potentially provide insight on the topology of these chemical structures.