Malaysian Journal of Mathematical Sciences, June 2026, Vol. 20, No. 2
Topological Aspects of Certain Transition Metals via Neighbourhood \(M-\)Polynomial
Ahmad, M., Saleem, M., Ghareeb, S., Qayyum, A., Alsulami, I. K.
Corresponding Email: dratherqayyum@um.edu.my
Received date: 28 June 2025
Accepted date: 30 September 2025
Abstract:
Graph theory is extensively used in chemistry for modeling molecular structures, resulting in the formation of molecular graphs. These molecular graphs serve as a crucial link between mathematics and the natural sciences. By associating chemical networks with molecular characteristics, they facilitate the design of biologically active substances through quantitative structure-activity relationship studies. One of the fundamental tools for investigating such relationships is the use of topological indices. These indices can be derived through mathematical operations involving polynomials. Among the existing techniques for structural characterization of molecular graphs, the approach based on neighborhood \(M-\)polynomials proves to be particularly effective. The neighborhood \(M-\)polynomials offer significant advantages in identifying structural patterns, analyzing molecular configurations, encoding structural information, evaluating structural variance under graph isomorphisms and acting as mathematical descriptors in quantitative structure-activity relationship investigations. They are essential in predicting biological activities and, more importantly, in designing new molecules with specific desired properties. Transition metals such as zinc (II), manganese (II), cobalt (II) and copper (II) are well-known for their extraordinary properties, which have attracted significant attention in medicine, food industries and production industries. This article aims to mathematically depict the above-mentioned transition metals through the use of neighborhood \(M-\)polynomials.
Keywords: zinc (II); Mn(II); neighborhood \(M-\)polynomials; cobalt (II) and copper (II)
