Fault-tolerant resolvability of some graphs of convex polytopes

IF 0.3 Q4 MATHEMATICS, APPLIED
S. Sharma, H. Raza, V. K. Bhat
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引用次数: 1

Abstract

Abstract The fault-tolerant resolvability is an extension of metric resolvability in graphs with several intelligent systems applications, for example, network optimization, robot navigation, and sensor networking. The graphs of convex polytopes, which are rotationally symmetric, are essential in intelligent networks due to the uniform rate of data transformation to all nodes. A resolving set is an ordered set 𝕎 of vertices of a connected graph G in which the vector of distances to the vertices in 𝕎 uniquely determines all the vertices of the graph G. The minimum cardinality of a resolving set of G is known as the metric dimension of G. If 𝕎 ∖ ρ is also a resolving set for each ρ in 𝕎. In that case, 𝕎 is said to be a fault-tolerant resolving set. The fault-tolerant metric dimension of G is the minimum cardinality of such a set 𝕎. The metric dimension and the fault-tolerant metric dimension for three families of convex polytope graphs are studied. Our main results affirm that three families, as mentioned above, have constant fault-tolerant resolvability structures.
一些凸多面体图的容错可分解性
容错可解析性是度量可解析性在图中的扩展,在网络优化、机器人导航和传感器网络等智能系统中有广泛的应用。由于数据到所有节点的转换速率一致,凸多面体图是旋转对称的,在智能网络中是必不可少的。解析集是连通图G的顶点的有序集,其中到顶点的距离向量唯一地决定了图G的所有顶点。G的解析集的最小基数被称为G的度量维数。如果∈ρ也是中每个ρ的解析集。在这种情况下,说它是一个容错解析集。G的容错度量维数是这样一个集合的最小基数。研究了三种凸多面体图族的度量维数和容错度量维数。我们的主要结果证实,如上所述,三个家庭具有恒定的容错可解性结构。
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来源期刊
CiteScore
0.60
自引率
20.00%
发文量
29
期刊介绍: The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.
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