On the Metric Dimension of Generalized Petersen Multigraphs
Muhammad Imran, Muhammad Kamran Siddiqui, Rishi Naeem · IEEE Access · 2018
In this paper, we study the metric dimension of barycentric subdivision of Möbius ladders and the metric dimension of generalized Petersen multigraphs. We prove that the generalized Petersen multigraphs denoted by$P(2n,n)$have metric dimension 3 when$n$is even and 4 otherwise. We also study the exchange property for resolving sets of barycentric subdivisions of Möbius ladders and generalized Petersen multigraphs and prove that the exchange property of the bases in a vector space does not hold for minimal resolving sets of these graphs.