Truncated metric dimension of graphsMrhar, Nik (Avtor) Bujtás, Csilla (Mentor) k-truncated metric dimensionresolving settadpole graphsubdivided starmulti-tailed tadpole graphgeneralised tadpole graphapproximation algorithmThe $k$-truncated metric dimension is a variant of the metric dimension in which distances greater than $k$ are treated as equal. In this thesis, we study the $k$-truncated metric dimension of several graph classes. We determine its exact value for tadpole graphs, subdivided stars, and multi-tailed tadpole graphs whose pendant paths have order at least $k+1$ after applying the reduction. We also consider generalised tadpole graphs, in which pendant paths satisfying the same condition may be attached to arbitrary vertices of a cycle. For this class, we develop a greedy algorithm for constructing a $k$-truncated resolving set. We prove the correctness of the algorithm, show that it runs in polynomial time for fixed $k$, and establish an approximation ratio of $4/3$.20262026-09-23 08:15:13Magistrsko delo/naloga188447sl