Abstract
The idea of a minimal resolving set has been used in a variety of contexts, including coin weighing, mastermind games, robot navigation, networking, and optimization. An NP-complete problem is determining the connected metric dimension of a given graph. In this study, we determine the exact value of the connected metric dimension for a number of trees, including Y-tree network, subdivision of Y-tree network, F-tree network, a subdivision of the F-tree network and the coconut network . Finally, we derive the explicit formulas for the subdivision of the -fire cracker and the subdivision of the coconut tree .
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