Journals Information
Mathematics and Statistics Vol. 13(4), pp. 218 - 227
DOI: 10.13189/ms.2025.130405
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On Achromatic Pseudoachromatic Number of Cellular Neural Networks
T. Kalaiselvi 1, Yegnanarayanan Venkataraman 1,*, Mark Sepanski 2, Rajermani Thinakaran 3
1 Department of Mathematics, Kalasalingam Academy of Research and Education, Krishnankoil, 626126, Tamil Nadu, India
2 Baylor University, Waco, TX-76706, USA
3 Faculty of Data Science & Information Technology, INTI International University, Negeri Sembilan, Malaysia
ABSTRACT
A motivation for this work stems from the fact that networks can be visualized as graphs with vertices of a graph as processing nodes and the edges as communication links. It is a known fact that graphs are utilized as a great visualizing tool and are widely involved in the task of characterizing the networks as interconnection parallel architectures, data routing schemes, computational workload etc. Inspired by the recent success of computation of graph-based indices for cellular neural networks and 3-layered or 4-layered probabilistic neural networks, a new attempt is made to identify the hidden symmetric structures on each of these networks and find the precise values of pseudoachromatic and achromatic numbers of the above mentioned networks as they yield vital counsel on topological and structural attributes of neural networks. A cellular neural network of dimension 
, denoted by 
is a strong product of two path graphs 
and 
. We probed the pseudoachromatic number and achromatic number of 
and derived tight lower and upper bounds of these parameters for . We also explained the theoretical and practical importance of these coloring parameters as process innovation and also raised some open problems.
KEYWORDS
Cellular Neural Networks, Achromatic Number, Pseudoachromatic Number
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] T. Kalaiselvi , Yegnanarayanan Venkataraman , Mark Sepanski , Rajermani Thinakaran , "On Achromatic Pseudoachromatic Number of Cellular Neural Networks," Mathematics and Statistics, Vol. 13, No. 4, pp. 218 - 227, 2025. DOI: 10.13189/ms.2025.130405.
(b). APA Format:
T. Kalaiselvi , Yegnanarayanan Venkataraman , Mark Sepanski , Rajermani Thinakaran (2025). On Achromatic Pseudoachromatic Number of Cellular Neural Networks. Mathematics and Statistics, 13(4), 218 - 227. DOI: 10.13189/ms.2025.130405.