Abstract
A directed Cayley graph Cay(Γ,X) is specified by a group Γ and an identity-free generating set X for this group. Vertices of Cay(Γ,X) are elements of Γ and there is a directed edge from a vertex u to a vertex v in Cay(Γ,X) if and only if there is a generator x∈X such that ux=v. We study the metric dimension for the directed Cayley graphs Cay(Γs,{a,b}) of general split metacyclic groups, and present the exact values of the metric dimension for the special split metacyclic groups Γs=〈a,b|an=b2s=1,ba=a−1b〉.
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