Abstract
The concept of M-polynomials determines the algebraic form of a system or network. It creates a structure into an algebraic equation and makes work easy to do on such a structure. This has diverse uses in different applied mathematics and as well as in engineering fields. In this study, we look closely at the abstract form of Y-shaped junctions. For the generic view of Y-shaped junctions, we developed some vertex-degree-based M-polynomials formulas. On Y-shaped junctions, we discussed some topological index-based concepts as well and verified the results available in the literature.