The solid-metric dimension

Abstract

<p>Resolving sets are designed to locate an object in a network by measuring the distances to the object. However, if there are more than one object present in the network, this can lead to wrong conclusions. To overcome this problem, we introduce the concept of solid-resolving sets. In this paper, we study the structure and constructions of solid-resolving sets. In particular, we classify the forced vertices with respect to a solid-resolving set. We also give bounds on the solid-metric dimension utilizing concepts like the Dilworth number, the boundary of a graph, and locating-dominating sets. It is also shown that deciding whether there exists a solid-resolving set with a certain number of elements is an NP-complete problem.<br></p>