Fault-tolerant metric dimension of graphs

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August undefined, 2024

WebNov 1, 2009 · They also proved that fault-tolerant metric dimension is bounded by a function of the metric dimension irrespective of the choice of the graph given beβ(G) ≤ β(G)(1 + 2.5 β(G)−1 ). 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

(PDF) Fault-Tolerant Metric Dimension of Graphs

WebFeb 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 … WebAug 7, 2024 · Fault-Tolerant Metric Dimension of Interconnection Networks. Abstract: A fixed interconnection parallel architecture is characterized by a graph, with vertices … diagram of climate and weather

Fault-Tolerant Distance Labeling for Planar Graphs Structural ...

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. 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 ... WebSep 9, 2014 · In this paper, we consider three similar optimization problems: the fault-tolerant metric dimension problem, the local metric dimension problem and the … diagram of circular saw

Fault-tolerant metric dimension of graphs — Monash University

The Fault-Tolerant Metric Dimension of Cographs

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 … WebAug 25, 2024 · A 2 − resolving set of minimum cardinality is called a 2 − metric basis of G and its cardinality is called the 2 − metric dimension (fault-tolerant metric dimension). … diagram of client serverWebThe Fault-Tolerant Metric Dimension of Cographs; Article . Free Access. The Fault-Tolerant Metric Dimension of Cographs ... diagram of client server architecture

"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. " - Fault-tolerant metric dimension of graphs

Fault-tolerant metric dimension of graphs

Fault-tolerant edge metric dimension of certain families …

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 ... WebJan 1, 2024 · A resolving set S for G is fault-tolerant if S \ {x} is also a resolving set, for each x in S, and the fault-tolerant metric dimension of G, denoted by β ′ (G), is the …

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WebThis book constitutes the proceedings of the 22nd International Symposium on Fundamentals of Computation Theory, FCT 2024, held in Copenhagen, Denmark, in August 2024. WebSep 9, 2014 · Ars Comb. In this paper, we consider three similar optimization problems: the fault-tolerant metric dimension problem, the local metric dimension problem and the strong metric dimension problem. These problems have applications in many diverse areas, including network discovery and verification, robot navigation and chemistry, etc.

WebIn this article, we study the metric and fault-tolerant dimension of certain families of interconnection networks. In particular, we focus on the fault-tolerant metric dimension … 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 .

WebIn this paper, fault-tolerant metric dimension problem (FTMDP) is considered. The existing integer linear programing (ILP) formulation, from the literature is improved, using … WebOct 31, 2024 · The results we obtained on the 48-node graphs we analyzed show a dependence between the quality of the optimization and the topology of the graph and in particular its dependence on the average degree 〈 k 〉. In order to reduce the influence of the finite size in the network models we have been using, we repeat the procedure for …

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.

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 ... cinnamon marshmallow clustersWebThe 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. cinnamon market priceWebThe fault-tolerant metric dimension of G is the minimum cardinality of a fault-tolerant resolving set, and it will be denoted by ﬂ0(G). A fault-tolerant resolving set of order … diagram of clinical thermometerWebMay 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 … cinnamon marshmallow cerealWebHome; Browse by Title; Proceedings; Structural Information and Communication Complexity: 28th International Colloquium, SIROCCO 2024, Wrocław, Poland, June 28 ... diagram of colon and anusWebSep 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 ... diagram of closed circuitWebSep 26, 2024 · Here, we determine the fault-tolerant metric dimension in line graphs. The fault-tolerant metric dimension in line graphs is only known for path and cycle graphs as … diagram of coccyx and sacral area skin