The monophonic pebbling number of neural networks with generalized algorithm and their applications

Articles in Press

Document Type : Original paper

Authors

Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology Vellore - 632014, Tamil Nadu, India

Abstract

Consider a graph σ(V, E) with nodes V and edges E is a connected graph with some pebbles scattered over its nodes V. By removal of two pebbles from one node and placing one pebble to an adjacent node is a pebbling move. A monophonic pebbling number, λM(σ,v), of a node v of a graph σ is the least number m such that minimum of one pebble could be shifted to v by a sequence of pebbling shifts for any distribution of λM(σ,v) pebbles on the nodes of σ using monophonic path. A link between the nodes x and y is an x-y path which consists of no chords and is monophonic. The monophonic pebbling number of a graph σ is the highest λM(σ,v) among all the nodes notated as λM(σ). For the first time, we calculate the monophonic pebbling number on families of neural networks such as probabilistic neural networks(PNNs),  convolutional neural networks(CVNNs), modular neural networks(MNNs), generalized regression neural networks(GRNNs) and Hopfield neural networks(HNNs) and discuss their applications. We give the generalized algorithm to find the monophonic pebbling number of any graph σ.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 28 September 2024

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