Results 11 to 20 of about 429,051 (306)

Edge Metric Dimension of Some Graph Operations [PDF]

Bulletin of the Malaysian Mathematical Sciences Society, 2019
Let $G=(V, E)$ be a connected graph. Given a vertex $v\in V$ and an edge $e=uw\in E$, the distance between $v$ and $e$ is defined as $d_G(e,v)=\min\{d_G(u,v),d_G(w,v)\}$. A nonempty set $S\subset V$ is an edge metric generator for $G$ if for any two edges $e_1,e_2\in E$ there is a vertex $w\in S$ such that $d_G(w,e_1)\ne d_G(w,e_2)$.
Iztok Peterin, Ismael G. Yero
semanticscholar   +6 more sources

Edge metric dimension of some classes of circulant graphs [PDF]

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020
Let G = (V (G), E(G)) be a connected graph and x, y ∈ V (G), d(x, y) = min{ length of x − y path } and for e ∈ E(G), d(x, e) = min{d(x, a), d(x, b)}, where e = ab. A vertex x distinguishes two edges e1 and e2, if d(e1, x) ≠ d(e2, x). Let WE = {w1, w2, . .
Ahsan Muhammad, Zahid Zohaib, Zafar Sohail   +2 more
doaj   +3 more sources

The local edge metric dimension of graph

Journal of Physics: Conference Series, 2020
Abstract In this paper, we introduce a new notion of graph theory study, namely a local edge metric dimension. It is a natural extension of metric dimension concept. dG (e,v) = min{d(x,v),d(y,v)} is the distance between the vertex v and the edge xy in graph G. A non empty set
Robiatul Adawiyah, Dafik Dafik, Ridho Alfarisi, Rafiantika Megahnia Prihandini, Ika Hesti Agustin, M. Venkatachalam   +5 more
semanticscholar   +3 more sources

On Some families of Path-related graphs with their edge metric dimension

Examples and Counterexamples
Locating the origin of diffusion in complex networks is an interesting but challenging task. It is crucial for anticipating and constraining the epidemic risks. Source localization has been considered under many feasible models.
Lianglin Li, Shu Bao, Hassan Raza
doaj   +4 more sources

Investigating Metric Dimension and Edge Metric Dimension of Hexagonal Boron Nitride and Carbon Nanotubes

European Journal of Pure and Applied Mathematics
When there is a difference in the distance between two vertices in a simple linked graph, then a vertex $x$ resolves both $u$ and $v$. If at least one vertex in $S$ distinguishes each pair of distinct vertices in $G$, then a set $S$ of vertices in $G$ is referred to as a resolving set.
Waseem Abbas, Faryal Chudhary, Umar Farooq, Muhammad Azeem, Yilun Shang   +4 more
semanticscholar   +3 more sources

Edge Metric Dimension of Some Generalized Petersen Graphs [PDF]

Results in Mathematics, 2019
The edge metric dimension problem was recently introduced, which initiated the study of its mathematical properties. The theoretical properties of the edge metric representations and the edge metric dimension of generalized Petersen graphs $GP(n,k)$ are studied in this paper. We prove the exact formulae for $GP(n,1)$ and $GP(n, 2)$, while for the other
Vladimir Filipović, Aleksandar Kartelj, Jozef Kratica, Vladimir Filipović, Aleksandar Kartelj, Jozef Kratica   +5 more
semanticscholar   +6 more sources

Edge based metric dimension of various coffee compounds.

PLoS ONE
An important dietary source of physiologically active compounds, coffee also contains phenolic acids, diterpenes, and caffeine. According to a certain study, some coffee secondary metabolites may advantageously modify a number of anti-cancer defense ...
Ali Ahmad, Ali N A Koam, Muhammad Azeem, Ibtisam Masmali, Rehab Alharbi   +4 more
doaj   +4 more sources

Graphs with the edge metric dimension smaller than the metric dimension [PDF]

Applied mathematics and computation, 2021
Given a connected graph G, the metric (resp. edge metric) dimension of G is the cardinality of the smallest ordered set of vertices that uniquely identifies every pair of distinct vertices (resp. edges) of G by means of distance vectors to such a set. In this work, we settle three open problems on (edge) metric dimension of graphs.
Knor, Martin, Majstorović, Snježana, Masa Toshi, Aoden Teo, Škrekovski, Riste, Yero, Ismael G.   +4 more
semanticscholar   +5 more sources

Metric and Edge Metric Dimension of Zigzag Edge Coronoid Fused with Starphene [PDF]

, 2021
Let $ =(V,E)$ be a simple connected graph. $d( , )=min\{d( , w), d( , d\}$ computes the distance between a vertex $ \in V( )$ and an edge $ =wd\in E( )$. A single vertex $ $ is said to recognize (resolve) two different edges $ _{1}$ and $ _{2}$ from $E( )$ if $d( , _{2})\neq d( , _{1}\}$.
Sunny Kumar Sharma, Vijay Kumar Bhat, Hassan Raza, Karnika Sharma   +3 more
  +5 more sources

Fault-tolerant edge metric dimension of certain families of graphs

AIMS Mathematics, 2021
Let $W_E=\{w_1,w_2, \ldots,w_k\}$ be an ordered set of vertices of graph $G$ and let $e$ be an edge of $G$. Suppose $d(x,e)$ denotes distance between edge $e$ and vertex $x$ of $G$, defined as $d(e,x) = d(x,e) = \min \{d(x,a),d(x,b)\}$, where $e=ab$.
Xiaogang Liu, Muhammad Ahsan, Zohaib Zahid, Shuili Ren   +3 more
doaj   +2 more sources