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For applied scientists and engineers, graph theory is a strong and vital tool for evaluating and inventing solutions for a variety of issues. Graph theory is extremely important in complex systems, particularly in computer science. Many scientific areas use graph theory, including biological sciences, engineering, coding, and operational research. A strategy for the orthogonal labelling of a bipartite graph G with n edges has been proposed in the literature, yielding cyclic decompositions of balanced complete bipartite graphs K n , n by the graph G. A generalization to circulant-balanced complete multipartite graphs K n , n , ⋯ , n ⏟ m ; m , n ≥ 2 , is our objective here. In this paper, we expand the orthogonal labelling approach used to generate cyclic decompositions for K n , n to a generalized orthogonal labelling approach that may be used for decomposing K n , n , ⋯ , n ⏟ m . We can decompose K n , n , ⋯ , n ⏟ m into distinct graph classes based on the proposed generalized orthogonal labelling approach. [ABSTRACT FROM AUTHOR]