Authors: Danas Milivojević, Milica
Kratica, Jozef 
Savić, Aleksandar
Maksimović, Zoran Lj.
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Some New General Lower Bounds for Mixed Metric Dimension of Graphs
Journal: Filomat
Volume: 35
Issue: 13
First page: 4275
Last page: 4285
Issue Date: 1-Jan-2021
Rank: M22
ISSN: 0354-5180
DOI: 10.2298/FIL2113275M
A vertex w ∈ V resolves two elements x, y ∈ V ∪ E if d(w, x) ≠ d(w, y). The mixed resolving set is a set of vertices S, S ⊆ V if any two elements of E ∪ V are resolved by some element of S. The minimum cardinality of a mixed resolving set is called the mixed metric dimension of a graph G. This paper introduces three new general lower bounds for the mixed metric dimension of a graph. The exact values of mixed metric dimension for torus graph are determined using one of these lower bounds. Finally, some illustrative examples of these new lower bounds and those known in the literature are presented on a set of some well-known graphs.
Keywords: General lower bounds | mixed metric dimension | Mixed metric generator | Mixed resolving set | Torus graph
Publisher: University of Niš
Project: Mathematical Modelas and Optimization Methods on Large-Scale Systems 

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