A Non-linear Synapse Neural Network with O(N) Neurons for Graph Colouring

A feedback artificial neural network with nonlinear synaptic connections is proposed for the classical graph colouring problem. The network employs O(N) Neurons with O(N
²
) non-linear synapses for a graph with N nodes. The network has a transcendental energy function that is fundamentally different from Hopfield Network. The proposed network always converges to a feasible solution, with the number of assigned colours being nearly equal to the Chromatic number of the corresponding graph. HSPICE simulation confirms the functioning of the proposed circuit. The results are compared with the existing circuits to highlight the significant reduction in the number of colours required for colouring a given graph.