Abstract
An ordered set W={w1,…,wk}⊆V(G) of vertices of G is called a resolving set or locating set for G if every vertex is uniquely determined by its vector of distances to the vertices in W. A resolving set of minimum cardinality is called a basis for G and this cardinality is the metric dimension or location number of G, denoted by β(G).In this paper, we study the metric dimension of certain wheel related graphs, namely m-level wheels, an infinite class of convex polytopes and antiweb-gear graphs denoted by Wn,m,Qn and AWJ2n, respectively. We prove that these infinite classes of wheel related graphs have unbounded metric dimension. The study of an infinite class of convex polytopes generated by wheel, denoted by Qn also gives a negative answer to an open problem proposed by Imran et al. (2012) in [8]:Open Problem: Is it the case that the graph of every convex polytope has constant metric dimension?It is natural to ask for characterization of graphs with unbounded metric dimension.
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 callDisclaimer: 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.
