Metric dimension of Cayley digraphs of split metacyclic groups

A directed Cayley graph Cay(Gamma, X) is specified by a group Gamma and an identity-free generating set X for this group. Vertices of Cay(Gamma, X) are elements of Gamma and there is a directed edge from a vertex u to a vertex v in Cay(Gamma, X) if and only if there is a generator x is an element of X such that ux = v. We study the metric dimension for the directed Cayley graphs Cay(Gamma(s) , {a,b}) of general split metacyclic groups, and present the exact values of the metric dimension for the special split metacyclic groups Gamma(s) = < a, b vertical bar a(n) = b(2s) =1, ba = a(-1)b >. (C) 2019 Elsevier B.V. All rights reserved.