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ON METRIC DIMENSION OF FUNCTIGRAPHS [PDF]

Discrete Mathematics, Algorithms and Applications, 2013
The metric dimension of a graph G, denoted by dim (G), is the minimum number of vertices such that each vertex is uniquely determined by its distances to the chosen vertices. Let G1and G2be disjoint copies of a graph G and let f : V(G1) → V(G2) be a function. Then a functigraphC(G, f) = (V, E) has the vertex set V = V(G1) ∪ V(G2) and the edge set E = E(
Eroh, Linda, Kang, Cong X., Yi, Eunjeong
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Metric dimension and edge metric dimension of windmill graphs

AIMS Mathematics, 2021
Graph invariants provide an amazing tool to analyze the abstract structures of graphs. Metric dimension and edge metric dimension as graph invariants have numerous applications, among them are robot navigation, pharmaceutical chemistry, etc.
Pradeep Singh, Sahil Sharma, Sunny Kumar Sharma, Vijay Kumar Bhat   +3 more
doaj   +3 more sources

Metric and fault-tolerant metric dimension for GeSbTe superlattice chemical structure [PDF]

PLoS ONE, 2023
The concept of metric dimension has many applications, including optimizing sensor placement in networks and identifying influential persons in social networks, which aids in effective resource allocation and focused interventions; finding the source of ...
Liu Liqin, Khurram Shahzad, Abdul Rauf, Fairouz Tchier, Adnan Aslam   +4 more
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Metric Dimension Threshold of Graphs [PDF]

Journal of Mathematics, 2022
Let G be a connected graph. A subset S of vertices of G is said to be a resolving set of G, if for any two vertices u and v of G there is at least a member w of S such that du,w≠dv,w.
Meysam Korivand, Kazem Khashyarmanesh, Mostafa Tavakoli   +2 more
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On Adjacency Metric Dimension of Some Families of Graph [PDF]

Journal of Function Spaces, 2022
Metric dimension of a graph is a well-studied concept. Recently, adjacency metric dimension of graph has been introduced. A set Qa⊂VG is considered to be an adjacency metric generator for G if u1,u2∈V\Qa (supposing each pair); there must exist a vertex q∈
Ali N. A. Koam, Ali Ahmad, Muhammad Azeem, Adnan Khalil, Muhammad Faisal Nadeem   +4 more
doaj   +2 more sources

On the metric dimension and fractional metric dimension for hierarchical product of graphs [PDF]

Applicable Analysis and Discrete Mathematics, 2013
A set of vertices W resolves a graph G if every vertex of G is uniquely determined by its vector of distances to the vertices in W. The metric dimension for G, denoted by dim(G), is the minimum cardinality of a resolving set of G. In order to study the metric dimension for the hierarchical product Gu22 ? Gu11 of two rooted graphs Gu22 and Gu11, we
Feng, Min, Wang, Kaishun
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The Metric Dimension and Local Metric Dimension of Relative Prime Graph [PDF]

Cauchy: Jurnal Matematika Murni dan Aplikasi, 2020
This study aims to determine the value of metric dimensions and local metric dimensions of relative prime graphs formed from modulo  integer rings, namely . As a vertex set is  and  if  and  are relatively prime.
Inna Kuswandari, Fatmawati Fatmawati, Mohammad Imam Utoyo   +2 more
doaj   +2 more sources

Optimizing emergency response services in urban areas through the fault-tolerant metric dimension of hexagonal nanosheet [PDF]

Scientific Reports
In this work, we find the fault-tolerant metric dimension of a hexagonal nanosheet. This concept ensures robust identity of vertices inside a graph, even in situations in which a few resolving vertices fail.
Yaoyao Tu, Sikander Ali, Muhammad Azeem, Misbah Arshad, Ghulam Haidar, Hamdy Khamees Thabet   +5 more
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The dominant metric dimension of graphs [PDF]

Heliyon, 2020
The G be a connected graph with vertex set V(G) and edge set E(G). A subset S⊆V(G) is called a dominating set of G if for every vertex x in V(G)∖S, there exists at least one vertex u in S such that x is adjacent to u.
Liliek Susilowati, Imroatus Sa'adah, Ratna Zaidatul Fauziyyah, Ahmad Erfanian, Slamin   +4 more
doaj   +2 more sources

Metric, edge-metric, mixed-metric, and fault-tolerant metric dimensions of geometric networks with potential applications [PDF]

Scientific Reports
Resolvability parameters of graphs are widely applicable in fields like computer science, chemistry, and geography. Many of these parameters, such as the metric dimension, are computationally hard to determine. This paper focuses on Möbius-type geometric
Sakander Hayat, Rishi Naeem, Hafiz Muhammad Afzal Siddiqui, Amina Riaz, Muhammad Imran, Melaku Berhe Belay, Zeineb Klai   +6 more
doaj   +2 more sources