Abstract
For having an in-depth study and analysis of various network’s structural properties such as interconnection, extensibility, availability, centralization, vulnerability and reliability, we require distance based graph theoretic parameters. Numerous parameters like distance based dimensions help in designing queuing models in restaurants, public health and service facilities and production lines. Likewise, allocations of robots several production units are indebted to these. Moreover, chemists and druggists use these parameters in finding out new drug type and structural formula of a chemical compound. In this article, we are finding out the extremal values of local fractional metric dimension of a class of network bearing convex as well as symmetric properties known by the name of convex polytopes. Also we have related the significance of our findings towards the end of the manuscript in the form of fire exit plan. The same will serve as a guide for future architects in planning a floor with a conducive fire exit plan.
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