Bounds of Fractional Metric Dimension and Applications with Grid-Related Networks

Autor:	Ali H. Alkhaldi, Muhammad Kamran Aslam, Muhammad Javaid, Abdulaziz Mohammed Alanazi
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	connected networks metric dimension fractional metric dimension resolving neighbourhoods Mathematics QA1-939
Zdroj:	Mathematics, Vol 9, Iss 12, p 1383 (2021)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math9121383
Popis:	Metric dimension of networks is a distance based parameter that is used to rectify the distance related problems in robotics, navigation and chemical strata. The fractional metric dimension is the latest developed weighted version of metric dimension and a generalization of the concept of local fractional metric dimension. Computing the fractional metric dimension for all the connected networks is an NP-hard problem. In this note, we find the sharp bounds of the fractional metric dimensions of all the connected networks under certain conditions. Moreover, we have calculated the fractional metric dimension of grid-like networks, called triangular and polaroid grids, with the aid of the aforementioned criteria. Moreover, we analyse the bounded and unboundedness of the fractional metric dimensions of the aforesaid networks with the help of 2D as well as 3D plots.
Databáze:	Directory of Open Access Journals
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