Geodesic
Some new general lower bounds for mixed metric dimension of graphs
Filomat, Tome 35 (2021) no. 13, p. 4275

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DOI

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
DOI : 10.2298/FIL2113275M
Classification : 05C09, 05C12
Keywords: mixed metric dimension, mixed resolving set, mixed metric generator, torus graph, general lower bounds 
Milica Milivojević Danas; Jozef Kratica; Aleksandar Savić; Zoran Lj Maksimović. Some new general lower bounds for mixed metric dimension of graphs. Filomat, Tome 35 (2021) no. 13, p. 4275 . doi: 10.2298/FIL2113275M
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     title = {Some new general lower bounds for mixed metric dimension of graphs},
     journal = {Filomat},
     pages = {4275 },
     year = {2021},
     volume = {35},
     number = {13},
     doi = {10.2298/FIL2113275M},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2113275M/}
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