Product Signed Domination in Probabilistic Neural Networks

Domination plays a very important role in graph theory.It has a lot of applications in various fields like communication, social science, engineering, etc.Let = (, ) be a simple graph.A function : → {-1,1} is said to be a product signed dominating function if each vertex in satisfies the condition [] = ∏ () ∈[] = 1 where [] denotes the closed neighborhood of .The weight () of a function is defined as () = ∑ () ∈ .The product signed domination number of a graph is the minimum positive weight of a product signed dominating function and is denoted as *().Product signed dominating function assigns 1 or -1 to the nodes of the graph.This variation of dominating function has applications in social networks of people or organizations.Probabilistic Neural Network (PNN) was first proposed by Specht.This is a classifier that maps input patterns in a number of class levels and estimates the probability of a sample being part of learned theory.This paper studies the existence of product signed dominating functions in probabilistic neural networks and calculates the accurate values of product signed domination numbers of three layered and four layered probabilistic neural networks.