Metro Domination Number of Certain Graphs

MDN

Abstract

We study the metro domination number γ_β(G), defined as the minimum size of a dominating set that also resolves a connected, simple, finite graph G. We present explicit formulas for γ_β(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.