Abstract
Abstract Topological index (TI) is a numerical invariant that helps to understand the natural relationship of the physicochemical properties of a compound in its primary structure. George Polya introduced the idea of counting polynomials in chemical graph theory and Winer made the use of TI in chemical compounds working on the paraffin's boiling point. The literature of the topological indices and counting polynomials of different graphs has grown extremely since that time. Metal-organic network (MON) is a group of different chemical compounds that consist of metal ions and organic ligands to represent unique morphology, excellent chemical stability, large pore volume, and very high surface area. Working on structures, characteristics, and synthesis of various MONs show the importance of these networks with useful applications, such as sensing of different gases, assessment of chemicals, environmental hazard, heterogeneous catalysis, gas and energy storage devices of excellent material, conducting solids, super-capacitors and catalysis for the purification, and separation of different gases. The above-mentioned properties and physical stability of these MONs become a most discussed topic nowadays. In this paper, we calculate the M-polynomials and various TIs based on these polynomials for two different MONs. A comparison among the aforesaid topological indices is also included to represent the better one.
Highlights
Molecular hydrogen is an odorless, tasteless, colorless, nontoxic, nonmetallic, and nominal molecule in the world with very high flammability scale. It is a next-generation and environmental friendly source of fuel (Petit and Bandosz, 2009). It is useful in different fuel cells to power engine that is very beneficial for environment
The current guiding laws established by the US Energy Department, put the attention on the detecting speed of the tool which must be detect 1 per cent of volume of smell-less molecular hydrogen in air in just 60 seconds
Koo et al (2017) prepared a fast molecular hydrogen detecting instrument containing metal nodes and organic ligands recognized as Metal-organic network (MON) with the assistance of palladium (Pd) nanowires
Summary
Molecular hydrogen is an odorless, tasteless, colorless, nontoxic, nonmetallic, and nominal molecule in the world with very high flammability scale. It is a next-generation and environmental friendly source of fuel (Petit and Bandosz, 2009) As molecular hydrogen, it is useful in different fuel cells to power engine that is very beneficial for environment. Koo et al (2017) prepared a fast molecular hydrogen detecting instrument containing metal nodes and organic ligands recognized as MON with the assistance of palladium (Pd) nanowires. This instrument must sense of hydrogen leaking intensity less than one per cent in only seven seconds. A graph is simple and connected, having no loops and multiple edges
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