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The monophonic pebbling number of neural networks with generalized algorithm and their applications | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 07 مهر 1403 اصل مقاله (2 M) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29481.2017 | ||
| نویسندگان | ||
| K.C. Kavitha* ؛ S. Jagatheswari* | ||
| Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology Vellore - 632014, Tamil Nadu, India | ||
| چکیده | ||
| Consider a graph $\sigma$(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, $\lambda_{M}(\sigma, v)$, of a node v of a graph $\sigma$ 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 $\lambda_{M}(\sigma, v)$ pebbles on the nodes of $\sigma$ 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 $\sigma$ is the highest $\lambda_{M}(\sigma, v)$ among all the nodes notated as $\lambda_{M}(\sigma)$. 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 $\sigma$. | ||
| کلیدواژه‌ها | ||
| Monophonic pebbling number؛ (PNNs)؛ (CVNNs)؛ (MNNs)؛ (GRNNs) and (HNNs) | ||
| مراجع | ||
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