On local fractional metric dimensions of Mycielski's graphs
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Date
2022
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UMT Lahore
Abstract
Metric dimension is an effective tool to study different distance based problems in the field of telecommunication, robotics, computer networking, integer programming, chemistry and electrical networking. the fractional metric dimension is the latest developed form of the metric dimension that is frequently used for the non-integral linear programming problems. in this thesis we will compute local fractional metric dimension (lfmd) for two different classes of mycielski's graphs called by path mycielski and cycle mycielski in the form of lower and upper bounds.the bounded and unboundedness of the obtained results is also discussed.we developed the general formulas of upper and lower bounds of local fractional metric dimension of mycielski's path graph for n≤10 , n ≡ 0(mod4) and mycielski's cycle graph. all the obtained results are illustrated by the examples of particular graphs belonging to the understudied families of graphs.