On Resolvability Parameters of Some Wheel-Related Graphs

Abstract EN

Let G=V,E be a simple connected graph, w∈V be a vertex, and e=uv∈E be an edge.

The distance between the vertex w and edge e is given by de,w=mindw,u,dw,v, A vertex w distinguishes two edges e1, e2∈E if dw,e1≠dw,e2.

A set S is said to be resolving if every pair of edges of G is distinguished by some vertices of S.

A resolving set with minimum cardinality is the basis for G, and this cardinality is the edge metric dimension of G, denoted by edimG.

It has already been proved that the edge metric dimension is an NP-hard problem.

The main objective of this article is to study the edge metric dimension of some families of wheel-related graphs and prove that these families have unbounded edge metric dimension.

Moreover, the results are compared with the metric dimension of these graphs.