Powerful and maximal rational metric dimension of a wheel

Abstract

The rational distance from the vertex u to the vertex v in a graph G, denoted by d(v/u), is defined as the average distances from the vertex u to the closed neighbors of v if u 6= v, else it is 0. A subset S of vertices of G is called rational resolving set of G if for every pair u, v of distinct vertices in V−S, there is a w ∈ S such that d(u/w) ≠ d(v/w) in G. In this paper powerful and maximal rational resolving sets are introduced and minimum cardinality of such sets are computed for the wheel graphs.