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〉.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.