Fault-tolerant metric dimension of graphs

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August undefined, 2024

Webof fault-tolerant metric dimension in [7]. This concept is de ned as follows : A resolving set F of a graphs G is fault- tolerant if F \ {v} is also a resolving set, for every vertex v ∈ F. The fault-tolerant metric dimension of G, denoted by β′(G), is the minimum cardinality of a fault-tolerant resolving set. WebOver years, many efforts are made for the problem of constructing quality fault-tolerant virtual backbones in wireless network. In case that a wireless network consists of physically equivalent nodes, e.g., with the same communication range, unit disk ...

Fault-tolerant edge metric dimension of certain families …

WebApr 20, 2024 · Metric dimension of a graph or a structure is a resolvability parameter that has been applied in numerous applications of graph theory, ... M. Imran, and M. K. Siddiqui, “Fault-tolerant metric dimension of interconnection networks,” IEEE Access, vol. 8, pp. 145435–145445, 2024. View at: Publisher Site Google Scholar. WebIn this paper, we introduce a variant of strong metric dimension, called the fault-tolerant strong metric dimension. A strong resolving set S for G is fault-tolerant if S ∖ {s} is … mt olympus weather washington

Fault-Tolerant Metric Dimension of Circulant Graphs

WebMay 25, 2024 · The fault-tolerant metric dimension of graphs has been introduced by Hernando et al. back in 2008 as a natural extension of the metric dimension. The reader is referred to [32,33,34,35] for various … WebComputing Digraph Width Measures on Directed Co-Graphs.- Fault-tolerant parallel scheduling of arbitrary length jobs on a shared channel.- Rare Siblings Speed-up Deterministic Detection and Counting of Small Pattern Graphs.- Bivariate B-splines from convex pseudo-circle configurations.- The Fault-Tolerant Metric Dimension of Cographs. WebJul 10, 2024 · The weighted (fault-tolerant) metric dimension for a given cost function \(c: V \longrightarrow \mathbb {R}_+\) is the minimum weight of all (fault-tolerant) resolving sets. Deciding whether a given graph G has (fault-tolerant) metric dimension at most … Table 3. The table shows how \(r_{a,b,c,d}\) is computed for \(G = G_1 \cup G_2\).. … how to make screen 2 screen 1

The fault-tolerant metric dimension of the king’s graph

On the 2-metric resolvability of graphs - AIMS Mathematics

WebThe fault-tolerant metric dimension of line graphs of necklace and prism graphs is computed and it is shown that if any vertex is removed from a resolving set, then the resulting set is also a resolves set, called the fault-Tolerant resolving set. Web[8] Chaudhry M.A., Javaid I. and Salman M., Fault-tolerant metric and partition dimension of graphs, Util Math 83 (2010), 187 – 199. Google Scholar [9] Estrado-Moreno A., Rodriguez-Velaquez J.A. and Yero I.G., The–metric dimension of a graph, Applied Mathematics and Information Sciences 9 (6) (2015), 2829 – 2840. Google Scholar how to make screen 2 my main screenWebApr 11, 2024 · Due to the variety of metric dimension applications in different areas of sciences, many generalizations were proposed, fault‐tolerant metric dimension is one of them. how to make screen bigger in runelite

"WebNov 14, 2024 · Do you navigate arXiv using a screen reader or other assistive technology? Are you a professor who helps students do so? We want to hear from you. " - Fault-tolerant metric dimension of graphs

Fault-tolerant metric dimension of graphs

The Fault-Tolerant Metric Dimension of Cographs

WebIn 2008, Hernando et al. presented the notion of fault tolerant metric dimension of graphs. In 2015, Estrado-Moreno et al. presented the concept of metric. For , the metric dimension is known as fault tolerant metric dimension denoted by . Further study on metric dimension can be seen in [8, 9]. An important variant of metric basis is the ... WebCheckpoint location: For some output sinks where the end-to-end fault-tolerance can be guaranteed, specify the location where the system will write all the checkpoint information. This should be a directory in an HDFS-compatible fault-tolerant file system. The semantics of checkpointing is discussed in more detail in the next section. Output Modes

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Webity is the fault-tolerant metric dimension of G, denoted by β′(G). Slater [1] introduced the concept of a resolving set for a connected graph which was also independently dis- covered by Harary ...

WebJan 1, 2008 · The metric dimension of G is the minimum cardinality of a resolving set of G. In this paper we introduce the study of the fault-tolerant metric dimension of a graph. A resolving set S for G is ... WebOct 21, 2024 · To tackle this issue, the definition is known as fault-tolerant edge resolving set which is dealt with by eliminating any of the member from and still obtains the unique position of the entire edge set of a graph, symbolized as , and the minimum members in the set denoted as and named as fault-tolerant edge metric dimension.

WebMay 12, 2024 · A fault-tolerant resolving set of order β ′ (G) is called a fault-tolerant metric basis. Determining the fault-tolerant metric dimension of a graph is an … WebThis book constitutes the proceedings of the 22nd International Symposium on Fundamentals of Computation Theory, FCT 2024, held in Copenhagen, Denmark, in August 2024.

WebHernando, C, Mora, M, Slater, PJ & Wood, D 2008, Fault-tolerant metric dimension of graphs. in M Changat, S Klavzar & A Vijayakumar (eds), Convexity in Discrete Structures. International Press of Boston, Inc., Massachusetts USA, pp. 81 - 85, International Instructional Workshop on Convexity in Discrete Structures, Massachusetts USA, 1/01/08 .

WebSep 26, 2024 · As a main result, we computed the fault-tolerant metric dimension of line graphs of necklace and prism graphs (2010 Mathematics Subject Classification: 05C78). The necklace graph Nen. The line ... mt olympus wisconsin dells places to eatWebFeb 18, 2024 · We proposed a fault-tolerant self-stable system that allows for the detection of an interrupter even if one of the sensors in the chain fails. If the elimination of any element from a RS is still a RS, then the RS is considered as a fault-tolerant resolving set (FTRS), and the fault-tolerant metric dimension (FTMD) is its minimum cardinality. how to make screen bigger ctrlWebIn this paper, fault-tolerant metric dimension problem (FTMDP) is considered. The existing integer linear programing (ILP) formulation, from the literature is improved, using … how to make screen bigger shortcut keyWebApr 8, 2024 · A resolving set W for G is fault-tolerant if W\{w} is also a resolving set, for each w ∈ W, and the fault-tolerant metric dimension of G is the minimum cardinality of … mt olympus wisconsin dells deathWebSep 9, 2014 · In this paper, we consider three similar optimization problems: the fault-tolerant metric dimension problem, the local metric dimension problem and the … mto mandatory reportingWebMar 21, 2024 · The fault tolerant metric dimension of a network can be regarded as a process of uniquely identification of each node of a network in case a malfunction occurs … mt olympus wisconsin dells logoWebFeb 3, 2024 · The fault-tolerant metric dimension (FTMD), fault-tolerant metric basis (FTMB), and the fault-tolerant metric co-ordinates (i.e., \(\varphi _{f}(c D^{*})\), for a … mt olympus wisconsin dells rotating slide