THE ADJACENCY SPECTRUM OF THE K(n)(n+1)_α COMPLETE MULTIPARTITION GRAPH

A graph is a pair of sets (V, E). V is the set of vertices, and E is the set of edges. Graph theory development may be relevant to other areas of mathematics, such as algebra, which are interesting to discuss. A graph can be represented by an adjacency matrix (degree matrix and connectivity of adjacency matrix) whose eigenvalues can be computed. This work aims to find a pattern that will later be used as a theorem for the spectrum of the complete poly-divided graph K(n)(n+1)_α. The results of this study indicate that the general form of the spectrum of a complete multipartition graph K(n)(n+1)α can be used to develop a theorem focused on the spectrum of the dot connected matrix. For further research, it is suggested to continue the research by looking for theorems of various spectrums that can be obtained from the complete graph K(n)(n+1)α to make a complete graph image and find a program.