scholarly journals On the strong metric dimension of corona product graphs and join graphs

2013 ◽  
Vol 161 (7-8) ◽  
pp. 1022-1027 ◽  
Author(s):  
Dorota Kuziak ◽  
Ismael G. Yero ◽  
Juan A. Rodríguez-Velázquez
Keyword(s):  
Metric Dimension ◽  
Product Graphs ◽  
Strong Metric Dimension ◽  
Corona Product

scholarly journals Dimensi Metrik Kuat Lokal Graf Hasil Operasi Kali Kartesian

2020 ◽  
Vol 1 (2) ◽  
pp. 64
Author(s):  
Nurma Ariska Sutardji ◽  
Liliek Susilowati ◽  
Utami Dyah Purwati
Keyword(s):  
Graph Theory ◽  
Cartesian Product ◽  
Metric Dimension ◽  
Star Graph ◽  
Product Graph ◽  
Path Graph ◽  
Strong Metric Dimension ◽  
Metric Dimensions ◽  
Development Result ◽  
Corona Product

The strong local metric dimension is the development result of a strong metric dimension study, one of the study topics in graph theory. Some of graphs that have been discovered about strong local metric dimension are path graph, star graph, complete graph, cycle graphs, and the result corona product graph. In the previous study have been built about strong local metric dimensions of corona product graph. The purpose of this research is to determine the strong local metric dimension of cartesian product graph between any connected graph G and H, denoted by dimsl (G x H). In this research, local metric dimension of G x H is influenced by local strong metric dimension of graph G and local strong metric dimension of graph H. Graph G and graph H has at least two order.

scholarly journals On the metric dimension of corona product graphs

2011 ◽  
Vol 61 (9) ◽  
pp. 2793-2798 ◽  
Author(s):  
I.G. Yero ◽  
D. Kuziak ◽  
J.A. Rodríguez-Velázquez
Keyword(s):  
Metric Dimension ◽  
Product Graphs ◽  
Corona Product

scholarly journals On the Local Metric Dimension of Corona Product Graphs

2015 ◽  
Vol 39 (S1) ◽  
pp. 157-173 ◽  
Author(s):  
Juan A. Rodríguez-Velázquez ◽  
Gabriel A. Barragán-Ramírez ◽  
Carlos García Gómez
Keyword(s):  
Metric Dimension ◽  
Product Graphs ◽  
Corona Product

On the strong metric dimension of product graphs

2014 ◽  
Vol 46 ◽  
pp. 169-176
Author(s):  
Dorota Kuziak ◽  
Juan A. Rodríguez-Velázquez ◽  
Ismael G. Yero
Keyword(s):  
Metric Dimension ◽  
Product Graphs ◽  
Strong Metric Dimension

scholarly journals On the strong metric dimension of the strong products of graphs

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Dorota Kuziak ◽  
Ismael G. Yero ◽  
Juan A. Rodríguez-Velázquez
Keyword(s):  
Connected Graph ◽  
Metric Dimension ◽  
Np Hard ◽  
Factor Graphs ◽  
Resolving Set ◽  
Sharp Bounds ◽  
Strong Product ◽  
Product Graphs ◽  
Strong Metric Dimension

AbstractLet G be a connected graph. A vertex w ∈ V.G/ strongly resolves two vertices u,v ∈ V.G/ if there exists some shortest u-w path containing v or some shortest v-w path containing u. A set S of vertices is a strong resolving set for G if every pair of vertices of G is strongly resolved by some vertex of S. The smallest cardinality of a strong resolving set for G is called the strong metric dimension of G. It is well known that the problem of computing this invariant is NP-hard. In this paper we study the problem of finding exact values or sharp bounds for the strong metric dimension of strong product graphs and express these in terms of invariants of the factor graphs.

scholarly journals Dimensi Matriks Dan Dimensi Partisi Pada Graf Hasil Operasi Korona

2017 ◽  
Vol 4 (5) ◽  
Author(s):  
Yuni Listiana
Keyword(s):  
Ordered Set ◽  
Metric Dimension ◽  
Resolving Set ◽  
Product Graphs ◽  
Minimum Number ◽  
Partition Dimension ◽  
Corona Product

Let𝐺(𝑉,𝐸)is a connected graph.For an ordered set 𝑊={𝑤1,𝑤2,…,𝑤𝑘} of vertices, 𝑊⊆𝑉(𝐺), and a vertex 𝑣∈𝑉(𝐺), the representation of 𝑣 with respect to 𝑊 is the ordered k-tuple 𝑟(𝑣|𝑊)={𝑑(𝑣,𝑤1),𝑑(𝑣,𝑤2),…,𝑑(𝑣,𝑤𝑘)|∀𝑣∈𝑉(𝐺)}. The set W is called a resolving set of G if every vertex of G has a distinct representation. A resolving set containing a minimum number of vertices is called a basis for 𝐺. The metric dimension of 𝐺, denoted by 𝑑𝑖𝑚(𝐺), is the number of vertices in a basis of 𝐺. Then, for a subset S of V(G), the distance between u and S is 𝑑(𝑣,𝑆)=𝑚𝑖𝑛{𝑑(𝑣,𝑥)|∀𝑥∈𝑆,∀𝑣∈𝑉(𝐺)}. Let Π=(𝑆1,𝑆2,…,𝑆𝑙)be an ordered l-partition of V(G), for∀𝑆𝑙⊂𝑉(𝐺) dan𝑣∈𝑉(𝐺), the representation of v with respect to Π is the l-vector 𝑟(𝑣|Π)=(𝑑(𝑣,𝑆1),𝑑(𝑣,𝑆2),…,𝑑(𝑣,𝑆𝑙)). The set Π is called a resolving partition for G if the 𝑙−vector 𝑟(𝑣|Π),∀𝑣∈𝑉(𝐺)are distinct. The minimum l for which there is a resolving l-partition of V(G) is the partition dimension of G, denoted by 𝑝𝑑(𝐺). In this paper, we determine the metric dimension and the partition dimension of corona product graphs 𝐾𝑛⨀𝐾𝑛−1, and we get some result that the metric dimension and partition dimension of 𝐾𝑛⨀𝐾𝑛−1respectively is𝑛(𝑛−2) and 2𝑛−1, for𝑛≥3.Keyword: Metric dimention, partition dimenstion,corona product graphs

Closed formulae for the local metric dimension of corona product graphs

2014 ◽  
Vol 46 ◽  
pp. 27-34 ◽  
Author(s):  
G.A. Barragán-Ramírez ◽  
C. García Gómez ◽  
Juan A. Rodríguez-Velázquez
Keyword(s):  
Metric Dimension ◽  
Product Graphs ◽  
Corona Product

scholarly journals Strong metric dimension of rooted product graphs

2015 ◽  
Vol 93 (8) ◽  
pp. 1265-1280 ◽  
Author(s):  
Dorota Kuziak ◽  
Ismael G. Yero ◽  
Juan A. Rodríguez-Velázquez
Keyword(s):  
Metric Dimension ◽  
Product Graphs ◽  
Strong Metric Dimension
Sign in / Sign up

Export Citation Format

Share Document