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A chemical network is numerically represented by a topological index in chemical graph theory. As opposed to its chemical representation, a topological descriptor correlates with specific physical properties of the underlying chemical molecules. In this article, third type of hex-derived networks HDN3(r), THDN3(r), are described. The goal of this study is to develop some updated and closed formulas based on multiplicative graph invariants. Such as ordinary geometric-arithmetic (OGA), general version of harmonic index (GHI), sum connectivity index (SI), general sum connectivity index (GSI), first and second Gourava and hyper-Gourava indices, Shegehalli and Kanabur indices, first generalized version of Zagreb index (GZI), and forgotten index (FI) for the hex-derived HDN3(r), THDN3(r), networks. Moreover, various types of edge for computing have been discovered and analyzed along with the order and size. The calculation of multiplicative topological features in networks that are generated from hexagonal structures is the main task of this work. Gaining more insight into the structural characteristics and possible uses of these networks requires examining the interaction between topological aspects and multiplication processes. To interpret the chemical compounds', physical and biological attributes, we can integrate the analysis of the networks stated above with the chemical compounds and their graphical structures. These results can be utilized to evaluate the biological and physio-chemical activities of compounds.

Owing to the marine environmental pollution affected by cruises, the use of techniques to mitigate carbon dioxide emission (CO2) is vital. Since a quarter of the fuel energy input to the engine is lost, waste management for marine diesel engines can provide some valuable outputs by which the need for other energy conversion-based methods disappears. Hence, the current work proposes a novel model of waste heat recovery for a 1 MW marine diesel engine in a low-temperature framework by which outstanding results are predictable. The defined auxiliary model consists of an absorption power cycle and an ejector refrigeration cycle to produce useful electricity and cooling for air conditioning. This model is designed for the first time and comprehensively analyzed and optimized to set the most suitable state of operation. The potential of the model is measured through the exergy, environmental, economic, and net present value standpoints. Moreover, an advanced evolutionary algorithm based on the non-dominated sorting genetic algorithm-II is applied to reach the optimum cost and exergetic performance. The optimum state showed an exergy efficiency of 35.19 % and products’ specific cost of 53.01 $/GJ. Moreover, the optimum payback period and CO2 emission reduction equal 6.79 years and 21.5 kg/MWh, respectively.