Geodesic
On the Metric Dimension of Circulant Graphs with $2$ Generators
Kragujevac Journal of Mathematics, Tome 43 (2019) no. 1, p. 49

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

A set of vertices $W$ resolves a connected graph $G$ if every vertex of $G$ is uniquely determined by its vector of distances to the vertices in $W$. The~number of vertices in a smallest resolving set is called the metric dimension and it is denoted by $\dim(G)$. We study the~circulant graphs $C_n (2,3)$ with the vertices $v_0, v_1, v_2,\dots, v_{n-1}$ and the edges $v_i v_{i+2}, v_i v_{i+3}$, where $i = 0, 1, 2,\dots, n-1$, the indices are taken modulo $n$. We show that for $n \ge 26$ we have $\dim(C_n (2,3)) = 3$ if $n \equiv 4 \pmod 6$, $\dim(C_n (2,3)) = 4$ if $n \equiv 0, 1, 5 \pmod 6$ and $3 \le \dim (C_n(2,3)) \le 4$ if $n \equiv 2, 3 \pmod 6$.
Classification : 05C35 05C12
Keywords: Metric dimension, resolving set, circulant graph, distance 
@article{KJM_2019_43_1_a4,
     author = {L. du Toit and T. Vetr{\'\i}k},
     title = {On the {Metric} {Dimension} of {Circulant} {Graphs} with $2$ {Generators}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {49 },
     publisher = {mathdoc},
     volume = {43},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2019_43_1_a4/}
}
TY  - JOUR
AU  - L. du Toit
AU  - T. Vetrík
TI  - On the Metric Dimension of Circulant Graphs with $2$ Generators
JO  - Kragujevac Journal of Mathematics
PY  - 2019
SP  - 49 
VL  - 43
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KJM_2019_43_1_a4/
LA  - en
ID  - KJM_2019_43_1_a4
ER  - 
%0 Journal Article
%A L. du Toit
%A T. Vetrík
%T On the Metric Dimension of Circulant Graphs with $2$ Generators
%J Kragujevac Journal of Mathematics
%D 2019
%P 49 
%V 43
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KJM_2019_43_1_a4/
%G en
%F KJM_2019_43_1_a4
L. du Toit; T. Vetrík. On the Metric Dimension of Circulant Graphs with $2$ Generators. Kragujevac Journal of Mathematics, Tome 43 (2019) no. 1, p. 49 . http://geodesic.mathdoc.fr/item/KJM_2019_43_1_a4/