On a conjecture about the local metric dimension of graphs
Let \(G\) be a graph of order \(n\) and clique number \(k\). It was conjectured in [\textit{G. Abrishami} et al., Discrete Math. 345, No. 4, Article ID 112763, 10 p. (2022; Zbl 1482.05076)] that the local metric dimension of \(G\) is bounded from the above by \(\frac{k-1}{k}n\). This article proves this conjecture. It is further proved that equality is attained precisely for complete graphs.
scientific article; zbMATH DE number 7636970
scientific article