Affiliations: [a] Department Mathematics, Rajalakshmi Engineering College, Thandalam, Chennai, India
| [b] Department of Mathematics, Easwari Engineering College, Chennai, India
| [c] Department of Mathematics, Saveetha Engineering College, Thandalam, Chennai, India
| [d] Department of Mathematics, Universitas Airlangga, Surabaya, Indonesia
| [e] School of Mathematics and Physics, Anhui Jianzhu University, Hefei, P.R. China
Correspondence:
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Corresponding author. S. Prabhu, Department Mathematics, Rajalakshmi Engineering College, Thandalam, Chennai 602105, India. E-mail: [email protected].
Abstract: Power utilities must track their power networks to respond to changing demand and availability conditions to ensure effective and efficient operation. As a result, several power companies continuously employ phase measuring units (PMUs) to continuously check their power networks. Supervising an electric power system with the fewest possible measurement equipment is precisely the vertex covering graph-theoretic problems otherwise a variation of the dominating set problem, in which a set D is defined as a power dominating set (PDS) of a graph if it supervises every vertex and edge in the system with a couple of rules. If the distance vector eccentrically characterizes each node in G with respect to the nodes in R, then the subset R of V (G) is a resolving set of G. The problem of finding power dominating set and resolving set problems are proven to be NP-complete in general. The finite subset R of V (G) is said to be resolving-power dominating set (RPDS) if it is both resolving and power dominating set, which is another NP-complete problem. The ηp (G) is the minimal cardinality of an RPDS of a graph G. A neural network is a collection of algorithms that tries to figure out the underlying correlations in a set of data by employing a method that replicates how the human brain functions. Various neural networks have seen rapid progress in multiple fields of study during the last few decades, including neurochemistry, artificial intelligence, automatic control, and informational sciences. Probabilistic neural networks (PNNs) offer a scalable alternative to traditional back-propagation neural networks in classification and pattern recognition applications. They do not necessitate the massive forward and backward calculations that ordinary neural networks entail. This paper investigates the resolving-power domination number of probabilistic neural networks.
Keywords: Metric dimension, basis, phasor measurement unit, power domination, probabilistic neural network, resolving set