Decompositions of Circulant-Balanced Complete Multipartite Graphs Based on a Novel Labelling Approach. (18th July 2022) - El-Mesady, A.; Bazighifan, Omar
Abstract : 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.