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 DIMENSI METRIK KETETANGGAAN LOKAL GRAF HASIL OPERASI k-COMB

2019 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Fryda Arum Pratama ◽  
Liliek Susilowati ◽  
Moh. Imam Utoyo
Keyword(s):  
Complete Graph ◽  
Connected Graph ◽  
Metric Dimension ◽  
Star Graph ◽  
K Value ◽  
Product Graph ◽  
Path Graph ◽  
Dominating Number ◽  
Cycle Graph

Research on the local adjacency metric dimension has not been found in all operations of the graph, one of them is comb product graph. The purpose of this research was to determine the local adjacency metric dimension of k-comb product graph and level  comb product graph between any connected graph G and H. In this research graph G and graph H such as cycle graph, complete graph, path graph, and star graph. K-comb product graph between any graph G and H denoted by GokH. While level k comb product graph between any graph G and H denoted by GokH.In this research, local adjacency metric dimension of GokSm graph only dependent to multiplication of the cardinality of V(G) and many of k value, while GokKm graph and GokCm graph is dependent to dominating number of G and multiplication of the cardinality of V(G), many of k value, and local adjacency metric dimension of Km graph or Cm graph. And then, local adjacency metric dimension of GokSm graph only dependent to the cardinality of V(Gok-1Sm), while GokKm graph and GokCm graph is dependent to dominating number of G and multiplication of the local adjacency metric dimension of Km graph or Cm graph with cardinality of V(Gok-1Km) or V(Gok-1Cm). 

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

THE ISOPERIMETRIC NUMBER OF d–DIMENSIONAL k–ARY ARRAYS

1999 ◽  
Vol 10 (03) ◽  
pp. 289-300 ◽  
Author(s):  
M. CEMIL AZIZOĞLU ◽  
ÖMER EĞECIOĞLU
Keyword(s):  
Cartesian Product ◽  
Product Graph ◽  
Path Graph ◽  
Number Formula ◽  
Isoperimetric Number

The d–dimensional k-ary array [Formula: see text] is the d–fold Cartesian product graph of the path graph Pk with k vertices. We show that the (edge) isoperimetric number [Formula: see text] of [Formula: see text] is given by [Formula: see text] and identify the cardinalities and the structure of the isoperimetric sets. For odd k, the cardinalities of isoperimetric sets in [Formula: see text] are [Formula: see text], whereas every isoperimetric set for k even has cardinality [Formula: see text].

scholarly journals Hubungan Dimensi Metrik Ketetanggaan dan Dimensi Metrik Ketetanggan Lokal Graf Hasil Operasi Kali Korona

2020 ◽  
Vol 2 (1) ◽  
pp. 13
Author(s):  
Virdina Rahmayanti ◽  
Moh. Imam Utoyo ◽  
Liliek Susilowati
Keyword(s):  
Connected Graph ◽  
Basic Characteristic ◽  
Metric Dimension ◽  
Product Graph ◽  
Graph Operations ◽  
Trivial Graph ◽  
Corona Product

Adjacency metric dimension and local adjacency metric dimension are the development of metric dimension. The purpose of this research is to determine the adjacency metric dimension of corona graph between any connected graph G and non-trivial graph H denoted by dimA(G⊙H), to determine the local adjacency metric dimension of corona graph between any connected graph G and non-trivial graph H denoted by dimA,l(G⊙H), and to determine the correlation between adjacency metric dimension and local adjacency metric dimension of corona product graph operations. In this research, it is found out that the value of adjacency metric dimension of G⊙H graph is affected by the basic characteristic of H and the domination characteristic. Meanwhile, the value of local adjacency metric dimension of G⊙H graph is only affected by the basic characteristic of H Futhermore, it is found a correlation of adjacency metric dimension and local adjacency metric dimension of corona product graph between any connected graph G and non-trivial graph H.

scholarly journals IMPLEMENTASI ALGORITMA MODIFIKASI BROYDEN-FLETCHER-GOLDFARB-SHANNO (MBFGS)

2017 ◽  
Vol 4 (5) ◽  
Author(s):  
Rahmawati Erma Standsyah
Keyword(s):  
Metric Dimension ◽  
Combinatorial Search ◽  
Robotic Navigation ◽  
Resolving Set ◽  
Circle Graph ◽  
Path Graph ◽  
Corona Product

The concept of minimum resolving set has proved to be useful and or related to a variety of fields such as Chemistry, Robotic Navigation, and Combinatorial Search and Optimization. Two graph are path graph (𝑃𝑛) anf circle graph (𝐶𝑚). The corona product 𝑃𝑛 ⨀𝐶𝑚 is defined as the graph obtained from 𝑃𝑛and 𝐶𝑚 by taking one copi of 𝑃𝑛 and 𝑚1copies of 𝐶𝑚 and joining by an edge each vertex from the 𝑛𝑡ℎ copy of 𝑃𝑛 with the 𝑚𝑡ℎ vertex of 𝐶𝑚. 𝑃𝑛 ⨀ 𝐶𝑚 and 𝐶𝑚⨀𝑃𝑛 not commute to 𝑛≠𝑚, it is showed that order of graph 𝑃𝑛 ⨀ 𝐶𝑚 different with graph 𝐶𝑚⨀𝑃𝑛. Based on research obtained 𝑑𝑖𝑚(𝑃𝑛⨀𝐶𝑚)=𝑛.𝑑𝑖𝑚(𝑊1,𝑚) dan 𝑑𝑖𝑚(𝐶𝑚⨀𝑃𝑛)=𝑚.𝑑𝑖𝑚 (𝐾1+𝑃𝑛)Keyword : Resolving Sets, Metric Dimension, Path Graph, Circle Graph, Corona Graph

Metric and Strong Metric Dimension in Cozero-Divisor Graphs

2021 ◽  
Vol 18 (3) ◽  
Author(s):  
R. Nikandish ◽  
M. J. Nikmehr ◽  
M. Bakhtyiari
Keyword(s):  
Metric Dimension ◽  
Strong Metric Dimension
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