Fault-tolerant metric dimension of graphs
WebNov 11, 2024 · We also computed the fault-tolerant edge metric dimension of path, cycle, complete graph, cycle with chord graph, tadpole graph and kayak paddle graph. Discover the world's research 20+ … 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 …
Fault-tolerant metric dimension of graphs
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WebApr 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 … 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.
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 ... WebFault-tolerant metric dimension of graphs. C. Hernando, M. Mora, +1 author. D. Wood. Published 2003. Mathematics. An ordered set S of vertices in a graph G is said to …
WebWe show that the complete multipartite graphs also have the fault-tolerant metric dimension n, which provides an infinite family of counterexamples to the characterization. Furthermore, we find exact values of the metric, edge metric, mixed-metric dimensions, the domination number, locating-dominating number, and metric-locating-dominating ... 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 ...
WebApr 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.
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 ... other term for moving forwardWebHome; Browse by Title; Proceedings; Structural Information and Communication Complexity: 28th International Colloquium, SIROCCO 2024, Wrocław, Poland, June 28 ... other term for mostlyWebThe 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. rocking climbing shoesWebCheckpoint 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 other term for movedWebJul 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 \(G = G_1 \cup G_2\).. … rocking climbing indoorWebFeb 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 … rocking clockWebSep 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. other term for my girl