Using Multidimensional Matrices to Determine Graph Properties

Abstract

The need to determine the most appropriate data model increases, as the complexity of the designed computing systems and computer networks increases. The graph model is one of the main models for this kind of tasks. However, graphs are so complex for systems with many nodes, that heuristic methods, which are basic in graph theory, become too resource intensive. But it is possible to determine individual properties of graphs, as well as their parameters using the methods of the theory of multidimensional matrices, with significantly less computing power resources. This article discusses some properties of graphs that can be analyzed using the (λ,μ)-collapsed product of multidimensional matrices. The proofs of the correspondence of one of the numerical parameters of the vertices of the graph and the result of squaring the adjacency matrix of the graph are carried out. The parameters of the graph that do not affect its chromatic number are formulated, and an assumption is made about a possible relationship between the chromatic number and the number of odd cycles in the graph.

Keywords

• clique
• multidimensional matrices
• graph properties
• chromatic number
• cycles in a graph