Abstract
Polyphenyl is used in a variety of applications including high-vacuum devices, optics, and electronics, and in high-temperature and radiation-resistant fluids and greases, it has low volatility, ionizing radiation stability, and high thermal-oxidative properties. The structure of polyphenyls can be represented using a molecular graph, where atoms represent vertices and bonds between atom edges. In a chemical structure, an item/vertex v resolves two items v 1 and v 2 if d v 1 , v ≠ d v 2 , v ; similarly, the ordered subset ϕ of vertices resolves each pair of distinct vertices named as the resolving set, and its minimum cardinality is described as metric dimension. In the pharmaceutical industry, the competition to find new chemical entities for treating a disease dictates larger project teams that encompass more extensive and diverse synthetic efforts directed at increasingly complicated activity spectra. In this paper, we determine the metric dimension of para-, meta-, and ortho-polyphenyl structures, which are used for structure-activity analysis of these polyphenyl structures.
Highlights
Chemists require the mathematical representation of a chemical compound to work with the chemical structure
A set of selected atoms gave mathematical representations so that it gave distinct representations to distinct atoms of the structure. e chemical structure can be defined in the form of vertices, which mentions the atom and edges indicate the bonds types, respectively. us, a graph-theoretic analysis of this idea yields the representations of all vertices in a structure in such a way that different vertices have distinct representations with respect to some specific atoms of that structure. e following are some mathematical definitions to indicate these concepts
In 1976, the idea of metric dimension of a graph was individually introduced by Harary and Melter in [2], and these time metric generators were named as resolving sets
Summary
Muhammad Faisal Nadeem ,1 Mohsan Hassan, Muhammad Azeem ,2 Salah Ud-Din Khan, Mohammed Rafi Shaik ,4 Mohammed A. Polyphenyl is used in a variety of applications including high-vacuum devices, optics, and electronics, and in high-temperature and radiation-resistant fluids and greases, it has low volatility, ionizing radiation stability, and high thermal-oxidative properties. E structure of polyphenyls can be represented using a molecular graph, where atoms represent vertices and bonds between atom edges. An item/vertex v resolves two items v1 and v2 if d(v1, v) ≠ d(v2, v); the ordered subset φ of vertices resolves each pair of distinct vertices named as the resolving set, and its minimum cardinality is described as metric dimension. We determine the metric dimension of para-, meta-, and ortho-polyphenyl structures, which are used for structureactivity analysis of these polyphenyl structures
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