SPEKTRUM MATRIKS KETETANGGAAN GRAF CAYLEY PADA GRUP Z_n

Abstract

A Cayley graph is a graph that represents a group. Cayley graphs, just like the concept of graph theory, generally consist of vertex and edges, where the vertices are group elements while the edges is formed based on the generating set of group elements except the identity element. The Cayley graph can be represented as an adjacency matrix where the neighboring vertices are 1 and 0 if they are not. The matrix spectrum is a collection of eigenvalues with their multiplicities represented in a matrix. The purpose of this study is to determine the general pattern of Cayley graphs in group Zn and the spectrum of the adjacency matrix of Cayley graphs in group Zn. This research was conducted using literature study and the results obtained that the Cayley graph in group Zn is an ordered graph. The types of Cayley graphs in group Zn include nP2 graph, Cn graph, Kn graph, kKnk graph, 2Kn graph. The adjacency matrix spectrum of Cayley graphs in group Zn is obtained by utilizing the circulant matrix in its solution.

Keywords: Cayley Graph, Group Zn, Adjacency Matrix, Circulant Matrix, Matrix Spectrum.