In this paper we address the problem of single-source fault-tolerant reachability in directed graphs. Our objective is to construct a sparse subgraph that preserves the
Fault tolerant subgraph for single source reachability: generic and ...
2016年6月19日 · We address the problem of single source reachability (SSR) from s in presence of failures of vertices/edges. We show that for every k ≥ 1, there is a subgraph H of G with at most 2 k n edges that preserves the reachability from s even after the failure of any k edges.
In this paper we address the problem of single source fault tolerant reachability in directed graphs. The objective is to construct a sparse subgraph that preserves the reachability from a given fixed source seven
As mentioned above, the main motivation for the problem of constructing k-fault tolerant graphs is nding fault tolerant architectures. The graph Grepresents a desired interconnection and the graph T the actual fault tolerant network that implements it. The graph T can sustain any k node (processor) faults and still simulate the graph Gwith no ...
Computing Fault-Tolerant Metric Dimension of Connected Graphs
In this study, the mixed fault-tolerant dimension of rooted product of a graph with path graph with reference to a pendant vertex of path graph is determined. In general, the necessary and sufficient conditions for graphs of order at least 3 having mixed fault …
Fault tolerant supergraphs with automorphisms - ScienceDirect
2019年2月15日 · Given a graph Y on n vertices and a desired level of fault-tolerance k, an objective in fault-tolerant system design is to construct a supergraph X on n + k vertices such that the removal of any k nodes from X leaves a graph containing Y.
The Fault-Tolerant Metric Dimension of Cographs
2019年7月10日 · In this paper we show that the weighted fault-tolerant metric dimension problem can be solved in linear time on cographs and give an algorithm that computes a minimum weight fault-tolerant resolving set. We consider graphs \ (G= (V,E)\), where V is the set of vertices and E is the set of edges.
Fault-Tolerant Metric Dimension of Graphs - ResearchGate
2008年1月1日 · A resolving set F for the graph G is a fault-tolerant resolving set if for each v∈F, F∖{v} is also a resolving set for G. In this article, we determine an optimal fault-resolving set of r-th...
graph theory - Fault Tolerant MST - Mathematics Stack Exchange
2023年3月8日 · Assuming the original graph is itself 2-edge-connected, so is fault-tolerant in that sense, you would need to extend the MST to also be 2-edge-connected, i.e. to have every vertex on a cycle.
Fault-tolerant strong metric dimension of graphs
In 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 also a strong resolving set, for each s in S, and the fault-tolerant strong metric dimension of G is the minimum cardinality of such a set and is denoted by dim f s (G).
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