Metro Domination Number of Certain Graphs
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Abstract
We study the metro domination number γβ(G), defined as the minimum size of a dominating set that also resolves a connected, simple, finite graph G. We present explicit formulas for γβ(G) for four classical graph families—Fan graphs, Firecracker graphs, Banana trees, and Coconut trees—together with concise proofs and examples. The presentation unifies domination and metric-dimension arguments, producing statements that are consistent with recent developments in the literature.
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