Geodesic
The doubly metric dimension of corona product graphs
Filomat, Tome 37 (2023) no. 13, p. 4375

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

DOI

The doubly metric dimension of a connected graph G is the minimum cardinality of doubly resolving sets in it. It is well known that deciding the doubly metric dimension of G is NP-complete. The corona product G ⊙ H of two vertex-disjoint graphs G and H is defined as the graph obtained from G and H by taking one copy of G and |V(G)| copies of H, then joining the ith vertex of G to every vertex in the ith copy of H. In this paper some formulae on the doubly metric dimension of corona product G ⊙ H of graphs G and H are established in terms of the order of G with the adjacency dimension of H and the doubly metric dimension of K 1 ⊙ H, respectively. We determine both sharp upper and lower bounds on doubly metric dimension of corona product graphs with disconnected and connected coronas involved, respectively, and characterize the corresponding extremal graphs. We also characterize all graphs G of diameter two with doubly metric dimension two. Furthermore, the exact values are obtained for the doubly metric dimensions of corona product graphs, being the corona either a path or a cycle.
DOI : 10.2298/FIL2313375N
Classification : 05C12, 05C35, 05C76
Keywords: metric dimension, doubly metric dimension, adjacency dimension, corona product 
Kairui Nie; Kexiang Xu. The doubly metric dimension of corona product graphs. Filomat, Tome 37 (2023) no. 13, p. 4375 . doi: 10.2298/FIL2313375N
@article{10_2298_FIL2313375N,
     author = {Kairui Nie and Kexiang Xu},
     title = {The doubly metric dimension of corona product graphs},
     journal = {Filomat},
     pages = {4375 },
     year = {2023},
     volume = {37},
     number = {13},
     doi = {10.2298/FIL2313375N},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2313375N/}
}
TY  - JOUR
AU  - Kairui Nie
AU  - Kexiang Xu
TI  - The doubly metric dimension of corona product graphs
JO  - Filomat
PY  - 2023
SP  - 4375 
VL  - 37
IS  - 13
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2313375N/
DO  - 10.2298/FIL2313375N
LA  - en
ID  - 10_2298_FIL2313375N
ER  - 
%0 Journal Article
%A Kairui Nie
%A Kexiang Xu
%T The doubly metric dimension of corona product graphs
%J Filomat
%D 2023
%P 4375 
%V 37
%N 13
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2313375N/
%R 10.2298/FIL2313375N
%G en
%F 10_2298_FIL2313375N

Cité par Sources :