The fault‐tolerant beacon set of hexagonal Möbius ladder network.

In localization, some specific nodes (beacon set) are selected to locate all nodes of a network, and if an arbitrary node stops working and still selected nodes remain in the beacon set, then the chosen nodes are called fault‐tolerant beacon set. Due to the variety of metric dimension applications in different areas of sciences, many generalizations were proposed, fault‐tolerant metric dimension is one of them. A resolving (beacon) set Bf$$ {B}_f $$ is fault tolerant, if Bf\ν$$ {B}_f\backslash \nu $$ for each ν∈Bf$$ \nu \in {B}_f $$ is also a resolving set; it is also known as a fault‐tolerant beacon set; the minimum cardinality of such a beacon set is known as the fault‐tolerant metric dimension of a graph G$$ G $$. In this paper, we find the fault‐tolerant beacon set of hexagonal Möbius ladder network H(α,β)$$ H\left(\alpha, \beta \right) $$ and proved that all the different variations of α$$ \alpha $$ and β$$ \beta $$ in H(α,β)$$ H\left(\alpha, \beta \right) $$ has constant fault‐tolerant metric dimension. [ABSTRACT FROM AUTHOR]