Decompositions of Circulant-Balanced Complete Multipartite Graphs Based on a Novel Labelling Approach - A. El-Mesady; Omar Bazighifan (Journal of Function Spaces)
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 Kn,n by the graph G. A generalization to circulant-balanced complete multipartite graphs Kn,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 Kn,n to a generalized orthogonal labelling approach that may be used for decomposing Kn,n,⋯,n⏟m. We can decompose Kn,n,⋯,n⏟m into distinct graph classes based on the proposed generalized orthogonal labelling approach.